diff --git a/pyproject.toml b/pyproject.toml
index f1adbc1935..f91142ff77 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -57,7 +57,6 @@ warn_no_return = "False"
 # mypy --no-error-summary 2>&1 | tr ':' ' ' | awk '{print $1}' | sort | uniq | sed 's/\.py//g; s|src/||g;  s|\/|\.|g' | xargs -I {} echo '"{}",'
 module = [
     "pytorch_lightning.callbacks.progress.rich_progress",
-    "pytorch_lightning.trainer.trainer",
     "lightning_app.api.http_methods",
     "lightning_app.api.request_types",
     "lightning_app.cli.app-template.app",
diff --git a/src/lightning_lite/strategies/registry.py b/src/lightning_lite/strategies/registry.py
index 4b35e82e3a..e6ac3ee96f 100644
--- a/src/lightning_lite/strategies/registry.py
+++ b/src/lightning_lite/strategies/registry.py
@@ -82,7 +82,7 @@ class _StrategyRegistry(dict):
 
         return do_register
 
-    def get(self, name: str, default: Optional[Any] = None) -> Any:
+    def get(self, name: str, default: Optional[Strategy] = None) -> Strategy:  # type: ignore[override]
         """Calls the registered strategy with the required parameters and returns the strategy object.
 
         Args:
diff --git a/src/pytorch_lightning/callbacks/progress/base.py b/src/pytorch_lightning/callbacks/progress/base.py
index 4fd4597c99..7dc555ee76 100644
--- a/src/pytorch_lightning/callbacks/progress/base.py
+++ b/src/pytorch_lightning/callbacks/progress/base.py
@@ -222,7 +222,9 @@ class ProgressBarBase(Callback):
         if not trainer.is_global_zero:
             self.disable()
 
-    def get_metrics(self, trainer: "pl.Trainer", pl_module: "pl.LightningModule") -> Dict[str, Union[int, str]]:
+    def get_metrics(
+        self, trainer: "pl.Trainer", pl_module: "pl.LightningModule"
+    ) -> Dict[str, Union[int, str, float, Dict[str, float]]]:
         r"""
         Combines progress bar metrics collected from the trainer with standard metrics from get_standard_metrics.
         Implement this to override the items displayed in the progress bar.
diff --git a/src/pytorch_lightning/callbacks/stochastic_weight_avg.py b/src/pytorch_lightning/callbacks/stochastic_weight_avg.py
index 5f36096fa1..9f727072fb 100644
--- a/src/pytorch_lightning/callbacks/stochastic_weight_avg.py
+++ b/src/pytorch_lightning/callbacks/stochastic_weight_avg.py
@@ -160,6 +160,7 @@ class StochasticWeightAveraging(Callback):
         if len(trainer.lr_scheduler_configs) > 1:
             raise MisconfigurationException("SWA currently not supported for more than 1 `lr_scheduler`.")
 
+        assert trainer.max_epochs is not None
         if isinstance(self._swa_epoch_start, float):
             self._swa_epoch_start = int(trainer.max_epochs * self._swa_epoch_start)
 
@@ -189,6 +190,7 @@ class StochasticWeightAveraging(Callback):
             for lr, group in zip(self._swa_lrs, optimizer.param_groups):
                 group["initial_lr"] = lr
 
+            assert trainer.max_epochs is not None
             self._swa_scheduler = cast(
                 _LRScheduler,
                 SWALR(
diff --git a/src/pytorch_lightning/loops/dataloader/evaluation_loop.py b/src/pytorch_lightning/loops/dataloader/evaluation_loop.py
index bbd269b704..60125e1174 100644
--- a/src/pytorch_lightning/loops/dataloader/evaluation_loop.py
+++ b/src/pytorch_lightning/loops/dataloader/evaluation_loop.py
@@ -56,7 +56,7 @@ class EvaluationLoop(DataLoaderLoop):
         self._results = _ResultCollection(training=False)
         self._outputs: List[EPOCH_OUTPUT] = []
         self._logged_outputs: List[_OUT_DICT] = []
-        self._max_batches: List[int] = []
+        self._max_batches: List[Union[int, float]] = []
         self._has_run: bool = False
         self._data_fetcher: Optional[AbstractDataFetcher] = None
 
@@ -213,7 +213,7 @@ class EvaluationLoop(DataLoaderLoop):
         self._results.cpu()
         self.epoch_loop.teardown()
 
-    def _get_max_batches(self) -> List[int]:
+    def _get_max_batches(self) -> List[Union[int, float]]:
         """Returns the max number of batches for each dataloader."""
         if self.trainer.testing:
             max_batches = self.trainer.num_test_batches
diff --git a/src/pytorch_lightning/loops/dataloader/prediction_loop.py b/src/pytorch_lightning/loops/dataloader/prediction_loop.py
index dcd91ef058..5d25e13ddb 100644
--- a/src/pytorch_lightning/loops/dataloader/prediction_loop.py
+++ b/src/pytorch_lightning/loops/dataloader/prediction_loop.py
@@ -1,4 +1,4 @@
-from typing import Any, List, Optional, Sequence
+from typing import Any, List, Optional, Sequence, Union
 
 from torch.utils.data import DataLoader
 
@@ -52,7 +52,7 @@ class PredictionLoop(DataLoaderLoop):
         return length
 
     @property
-    def max_batches(self) -> List[int]:
+    def max_batches(self) -> List[Union[int, float]]:
         """The max number of batches this loop will run for each dataloader."""
         return self.trainer.num_predict_batches
 
diff --git a/src/pytorch_lightning/loops/epoch/training_epoch_loop.py b/src/pytorch_lightning/loops/epoch/training_epoch_loop.py
index 0877bb7347..1cf2a5a6de 100644
--- a/src/pytorch_lightning/loops/epoch/training_epoch_loop.py
+++ b/src/pytorch_lightning/loops/epoch/training_epoch_loop.py
@@ -292,6 +292,7 @@ class TrainingEpochLoop(loops.Loop[_OUTPUTS_TYPE]):
             # TODO: fault-tolerance requires a minimum number of batches so probably should be > 0
             and self.batch_progress.current.ready  # did start
         ):
+            assert isinstance(trainer.train_dataloader, CombinedLoader)
             loader: CombinedLoader = trainer.train_dataloader
             state = loader.state_dict(has_completed=self._has_completed())
             if state:
diff --git a/src/pytorch_lightning/loops/fit_loop.py b/src/pytorch_lightning/loops/fit_loop.py
index 48a5d1ef12..25b1bb8bc7 100644
--- a/src/pytorch_lightning/loops/fit_loop.py
+++ b/src/pytorch_lightning/loops/fit_loop.py
@@ -23,7 +23,7 @@ from pytorch_lightning.loops.epoch.training_epoch_loop import _OUTPUTS_TYPE as _
 from pytorch_lightning.loops.utilities import _is_max_limit_reached, _set_sampler_epoch
 from pytorch_lightning.trainer.connectors.logger_connector.result import _ResultCollection
 from pytorch_lightning.trainer.progress import Progress
-from pytorch_lightning.trainer.supporters import TensorRunningAccum
+from pytorch_lightning.trainer.supporters import CombinedLoader, TensorRunningAccum
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 from pytorch_lightning.utilities.fetching import (
     AbstractDataFetcher,
@@ -48,7 +48,7 @@ class FitLoop(Loop[None]):
 
     def __init__(
         self,
-        min_epochs: int = 0,
+        min_epochs: Optional[int] = 0,
         max_epochs: Optional[int] = None,
     ) -> None:
         super().__init__()
@@ -233,6 +233,7 @@ class FitLoop(Loop[None]):
         self._outputs = []
 
         if self.trainer.train_dataloader is not None:
+            assert isinstance(self.trainer.train_dataloader, CombinedLoader)
             _set_sampler_epoch(self.trainer.train_dataloader, self.epoch_progress.current.processed)
 
         # changing gradient according accumulation_scheduler
diff --git a/src/pytorch_lightning/loops/utilities.py b/src/pytorch_lightning/loops/utilities.py
index 3dcc2f6531..f60e00333e 100644
--- a/src/pytorch_lightning/loops/utilities.py
+++ b/src/pytorch_lightning/loops/utilities.py
@@ -14,7 +14,7 @@
 from collections import OrderedDict
 from contextlib import contextmanager
 from functools import lru_cache
-from typing import Any, Generator, List, Optional, Sequence, Tuple
+from typing import Any, Generator, List, Optional, Sequence, Tuple, Union
 
 import numpy as np
 import torch
@@ -29,6 +29,7 @@ from pytorch_lightning.loops import Loop
 from pytorch_lightning.strategies.parallel import ParallelStrategy
 from pytorch_lightning.strategies.strategy import Strategy
 from pytorch_lightning.trainer.progress import BaseProgress
+from pytorch_lightning.trainer.supporters import CombinedLoader
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 from pytorch_lightning.utilities.memory import recursive_detach
 from pytorch_lightning.utilities.rank_zero import rank_zero_warn
@@ -69,7 +70,11 @@ def _extract_hiddens(training_step_output: STEP_OUTPUT, truncated_bptt_steps: in
 
 
 def _parse_loop_limits(
-    min_steps: Optional[int], max_steps: int, min_epochs: Optional[int], max_epochs: int, trainer: "pl.Trainer"
+    min_steps: Optional[int],
+    max_steps: int,
+    min_epochs: Optional[int],
+    max_epochs: Optional[int],
+    trainer: "pl.Trainer",
 ) -> Tuple[int, int]:
     """This utility computes the default values for the minimum and maximum number of steps and epochs given the
     values the user has selected.
@@ -216,13 +221,14 @@ def _reset_progress(loop: Loop) -> None:
             _reset_progress(v)
 
 
-def _set_sampler_epoch(dataloader: DataLoader, epoch: int) -> None:
+def _set_sampler_epoch(dataloader: Union[DataLoader, CombinedLoader], epoch: int) -> None:
     """Calls the ``set_epoch`` method on either the sampler or the batch sampler of the given dataloader.
 
     Every PyTorch dataloader has either a sampler or a batch sampler, and if it is wrapped by a
     :class:`~torch.utils.data.distributed.DistributedSampler`, ``set_epoch`` must be called at the beginning
     of every epoch to ensure shuffling applies a new ordering. This has no effect if shuffling is off.
     """
+
     for sampler_name in ("sampler", "batch_sampler"):
         sampler = getattr(dataloader, sampler_name, None)
         if sampler is not None and callable(getattr(sampler, "set_epoch", None)):
diff --git a/src/pytorch_lightning/overrides/base.py b/src/pytorch_lightning/overrides/base.py
index 10ab5c06b2..c61d183974 100644
--- a/src/pytorch_lightning/overrides/base.py
+++ b/src/pytorch_lightning/overrides/base.py
@@ -101,6 +101,7 @@ class _LightningModuleWrapperBase(_DeviceDtypeModuleMixin, torch.nn.Module):
                 # `require_backward_grad_sync` will be reset in the
                 # ddp_strategy `post_training_step` hook
                 if not pl_module.automatic_optimization:
+                    assert trainer.model is not None
                     trainer.model.require_backward_grad_sync = False  # type: ignore[assignment]
                 return output
             if trainer.testing:
diff --git a/src/pytorch_lightning/trainer/connectors/accelerator_connector.py b/src/pytorch_lightning/trainer/connectors/accelerator_connector.py
index c74d1144f3..8ba07c53d7 100644
--- a/src/pytorch_lightning/trainer/connectors/accelerator_connector.py
+++ b/src/pytorch_lightning/trainer/connectors/accelerator_connector.py
@@ -109,7 +109,7 @@ class AcceleratorConnector:
         sync_batchnorm: bool = False,
         benchmark: Optional[bool] = None,
         replace_sampler_ddp: bool = True,
-        deterministic: Union[bool, _LITERAL_WARN] = False,
+        deterministic: Optional[Union[bool, _LITERAL_WARN]] = False,
         auto_select_gpus: bool = False,
         num_processes: Optional[int] = None,  # deprecated
         tpu_cores: Optional[Union[List[int], str, int]] = None,  # deprecated
@@ -663,7 +663,8 @@ class AcceleratorConnector:
         if isinstance(self._strategy_flag, str):
             self.strategy = StrategyRegistry.get(self._strategy_flag)
         elif isinstance(self._strategy_flag, Strategy):
-            self.strategy = self._strategy_flag
+            # TODO(lite): remove ignore after merging lite and PL strategies
+            self.strategy = self._strategy_flag  # type: ignore[assignment]
         else:
             raise RuntimeError(f"{self.strategy} is not valid type: {self.strategy}")
 
@@ -687,9 +688,7 @@ class AcceleratorConnector:
                     )
                 return TPUBf16PrecisionPlugin()
         if isinstance(self.strategy, DeepSpeedStrategy):
-            return DeepSpeedPrecisionPlugin(
-                self._precision_flag, self._amp_type_flag, self._amp_level_flag  # type: ignore
-            )
+            return DeepSpeedPrecisionPlugin(self._precision_flag, self._amp_type_flag, self._amp_level_flag)
 
         if self._precision_flag == 32:
             return PrecisionPlugin()
diff --git a/src/pytorch_lightning/trainer/connectors/data_connector.py b/src/pytorch_lightning/trainer/connectors/data_connector.py
index dce9a4fbaa..47aae74f15 100644
--- a/src/pytorch_lightning/trainer/connectors/data_connector.py
+++ b/src/pytorch_lightning/trainer/connectors/data_connector.py
@@ -57,23 +57,17 @@ class DataConnector:
     def _should_reload_train_dl(self) -> bool:
         """Check if train dataloader should be reloaded."""
         n_epochs = self.trainer.reload_dataloaders_every_n_epochs
-        return n_epochs and (
-            self.trainer._last_train_dl_reload_epoch is None
-            or self.trainer.current_epoch - self.trainer._last_train_dl_reload_epoch >= n_epochs
-        )
+        return n_epochs and self.trainer.current_epoch - self.trainer._last_train_dl_reload_epoch >= n_epochs
 
     @property
     def _should_reload_val_dl(self) -> bool:
         """Check if validation dataloader should be reloaded."""
         n_epochs = self.trainer.reload_dataloaders_every_n_epochs
-        return n_epochs and (
-            self.trainer._last_val_dl_reload_epoch is None
-            or self.trainer.current_epoch - self.trainer._last_val_dl_reload_epoch >= n_epochs
-        )
+        return n_epochs and self.trainer.current_epoch - self.trainer._last_val_dl_reload_epoch >= n_epochs
 
     def on_trainer_init(
         self,
-        val_check_interval: Union[int, float],
+        val_check_interval: Optional[Union[int, float]],
         reload_dataloaders_every_n_epochs: int,
         check_val_every_n_epoch: Optional[int],
     ) -> None:
@@ -347,7 +341,7 @@ class DataConnector:
 
     def _reset_eval_dataloader(
         self, mode: RunningStage, model: Optional["pl.LightningModule"] = None
-    ) -> Tuple[List[Union[int, float]], List[DataLoader]]:
+    ) -> Tuple[List[Union[float, int]], List[DataLoader]]:
         """Generic method to reset a dataloader for evaluation.
 
         Args:
@@ -387,7 +381,7 @@ class DataConnector:
             dataloaders, dtype=DataLoader, function=_auto_add_worker_init_fn, rank=self.trainer.global_rank
         )
 
-        loader_num_batches = []
+        loader_num_batches: List[Union[int, float]] = []
 
         # determine number of batches
         module = model or self.trainer.lightning_module or self.datamodule
@@ -398,6 +392,7 @@ class DataConnector:
                 )
 
                 if orig_num_batches == 0:
+                    assert isinstance(orig_num_batches, int)
                     loader_num_batches.append(orig_num_batches)
                     continue
 
diff --git a/src/pytorch_lightning/trainer/supporters.py b/src/pytorch_lightning/trainer/supporters.py
index 454143416f..c11756ed4b 100644
--- a/src/pytorch_lightning/trainer/supporters.py
+++ b/src/pytorch_lightning/trainer/supporters.py
@@ -28,7 +28,6 @@ from pytorch_lightning.utilities.auto_restart import (
     MergedIteratorState,
     patch_dataloader_iterator,
 )
-from pytorch_lightning.utilities.data import get_len
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 from pytorch_lightning.utilities.imports import _fault_tolerant_training
 
@@ -457,6 +456,8 @@ class CombinedLoader:
         Returns:
             the wrapped loaders
         """
+        from pytorch_lightning.utilities.data import get_len
+
         all_lengths = apply_to_collection(self.loaders, Iterable, get_len, wrong_dtype=(Sequence, Mapping))
 
         length = _nested_calc_num_data(all_lengths, max)
@@ -473,6 +474,8 @@ class CombinedLoader:
     def _apply_cycle_iterator_length(self) -> None:
         """When the model is `max_size_cycle`, compute the length across all ``CycleIterator`` and re-assign it to
         all dataloaders."""
+        from pytorch_lightning.utilities.data import get_len
+
         if self.mode != "max_size_cycle":
             return
 
@@ -509,6 +512,8 @@ class CombinedLoader:
         Returns:
             length: the minimum length of loaders
         """
+        from pytorch_lightning.utilities.data import get_len
+
         all_lengths = apply_to_collection(loaders, Iterable, get_len, wrong_dtype=(Sequence, Mapping))
 
         if isinstance(all_lengths, (int, float)):
diff --git a/src/pytorch_lightning/trainer/trainer.py b/src/pytorch_lightning/trainer/trainer.py
index 578b714eba..9e788929f7 100644
--- a/src/pytorch_lightning/trainer/trainer.py
+++ b/src/pytorch_lightning/trainer/trainer.py
@@ -25,7 +25,7 @@ import logging
 import math
 import os
 import warnings
-from argparse import ArgumentParser, Namespace
+from argparse import _ArgumentGroup, ArgumentParser, Namespace
 from contextlib import contextmanager
 from copy import deepcopy
 from datetime import timedelta
@@ -73,7 +73,7 @@ from pytorch_lightning.trainer.connectors.callback_connector import CallbackConn
 from pytorch_lightning.trainer.connectors.checkpoint_connector import CheckpointConnector
 from pytorch_lightning.trainer.connectors.data_connector import DataConnector
 from pytorch_lightning.trainer.connectors.logger_connector import LoggerConnector
-from pytorch_lightning.trainer.connectors.logger_connector.result import _ResultCollection
+from pytorch_lightning.trainer.connectors.logger_connector.result import _OUT_DICT, _PBAR_DICT, _ResultCollection
 from pytorch_lightning.trainer.connectors.signal_connector import SignalConnector
 from pytorch_lightning.trainer.states import RunningStage, TrainerFn, TrainerState, TrainerStatus
 from pytorch_lightning.trainer.supporters import CombinedLoader
@@ -457,7 +457,7 @@ class Trainer:
         self._call_callback_hooks("on_init_start")
 
         # init data flags
-        self.check_val_every_n_epoch: int
+        self.check_val_every_n_epoch: Optional[int]
         self._data_connector.on_trainer_init(
             val_check_interval,
             reload_dataloaders_every_n_epochs,
@@ -484,7 +484,7 @@ class Trainer:
                 f"`track_grad_norm` must be a positive number or 'inf' (infinity norm). Got {track_grad_norm}."
             )
 
-        self.gradient_clip_val: Union[int, float] = gradient_clip_val
+        self.gradient_clip_val: Optional[Union[int, float]] = gradient_clip_val
         self.gradient_clip_algorithm: Optional[GradClipAlgorithmType] = (
             GradClipAlgorithmType(gradient_clip_algorithm.lower()) if gradient_clip_algorithm is not None else None
         )
@@ -504,8 +504,13 @@ class Trainer:
         self._logger_connector.on_trainer_init(logger, log_every_n_steps, move_metrics_to_cpu)
 
         # init debugging flags
+        self.val_check_batch: Union[int, float]
         self.val_check_interval: Union[int, float]
-        self.num_sanity_val_steps: Union[float, int]
+        self.num_sanity_val_steps: Union[int, float]
+        self.limit_train_batches: Union[int, float]
+        self.limit_val_batches: Union[int, float]
+        self.limit_test_batches: Union[int, float]
+        self.limit_predict_batches: Union[int, float]
         setup._init_debugging_flags(
             self,
             limit_train_batches,
@@ -527,17 +532,19 @@ class Trainer:
         self.should_stop = False
         self.state = TrainerState()
         self.num_training_batches = float("inf")
-        self.train_dataloader = None
 
-        self.num_sanity_val_batches = []
-        self.num_test_batches = []
-        self.num_val_batches = []
-        self.num_predict_batches = []
-        self.test_dataloaders = None
-        self.val_dataloaders = None
-        self.predict_dataloaders = None
-        self._last_train_dl_reload_epoch = None
-        self._last_val_dl_reload_epoch: Optional[int] = None
+        self.train_dataloader: Optional[Union[CombinedLoader, TRAIN_DATALOADERS]] = None
+
+        self.num_sanity_val_batches: List[Union[int, float]] = []
+        self.num_test_batches: List[Union[int, float]] = []
+        self.num_val_batches: List[Union[int, float]] = []
+        self.num_predict_batches: List[Union[int, float]] = []
+
+        self.test_dataloaders: Optional[List[DataLoader]] = None
+        self.val_dataloaders: Optional[List[DataLoader]] = None
+        self.predict_dataloaders: Optional[List[DataLoader]] = None
+        self._last_train_dl_reload_epoch = float("-inf")
+        self._last_val_dl_reload_epoch = float("-inf")
 
     def fit(
         self,
@@ -605,13 +612,16 @@ class Trainer:
         # TODO: ckpt_path only in v2.0
         ckpt_path = ckpt_path or self.resume_from_checkpoint
         self._ckpt_path = self._checkpoint_connector._set_ckpt_path(
-            self.state.fn, ckpt_path, model_provided=True, model_connected=self.lightning_module is not None
+            self.state.fn,
+            ckpt_path,  # type: ignore[arg-type]
+            model_provided=True,
+            model_connected=self.lightning_module is not None,
         )
-        results = self._run(model, ckpt_path=self.ckpt_path)
+        self._run(model, ckpt_path=self.ckpt_path)
 
         assert self.state.stopped
         self.training = False
-        return results
+        return
 
     def validate(
         self,
@@ -659,7 +669,7 @@ class Trainer:
         ckpt_path: Optional[str] = None,
         verbose: bool = True,
         datamodule: Optional[LightningDataModule] = None,
-    ) -> _EVALUATE_OUTPUT:
+    ) -> Optional[Union[_PREDICT_OUTPUT, _EVALUATE_OUTPUT]]:
         # --------------------
         # SETUP HOOK
         # --------------------
@@ -751,7 +761,7 @@ class Trainer:
         ckpt_path: Optional[str] = None,
         verbose: bool = True,
         datamodule: Optional[LightningDataModule] = None,
-    ) -> _EVALUATE_OUTPUT:
+    ) -> Optional[Union[_PREDICT_OUTPUT, _EVALUATE_OUTPUT]]:
         # --------------------
         # SETUP HOOK
         # --------------------
@@ -853,7 +863,7 @@ class Trainer:
         self.state.status = TrainerStatus.RUNNING
         self.predicting = True
 
-        self.predict_loop.return_predictions = return_predictions
+        self.predict_loop.return_predictions = return_predictions  # type: ignore[assignment]
 
         # if a datamodule comes in as the second arg, then fix it for the user
         if isinstance(dataloaders, LightningDataModule):
@@ -1103,7 +1113,7 @@ class Trainer:
             logger.log_graph(self.lightning_module)
             logger.save()
 
-    def _teardown(self):
+    def _teardown(self) -> None:
         """This is the Trainer's internal teardown, unrelated to the `teardown` hooks in LightningModule and
         Callback; those are handled by :meth:`_call_teardown_hook`."""
         self.strategy.teardown()
@@ -1114,7 +1124,7 @@ class Trainer:
         self._logger_connector.teardown()
         self._signal_connector.teardown()
 
-    def _run_stage(self):
+    def _run_stage(self) -> Optional[Union[_PREDICT_OUTPUT, _EVALUATE_OUTPUT]]:
         self.strategy.barrier("run-stage")
         self.strategy.dispatch(self)
 
@@ -1122,9 +1132,9 @@ class Trainer:
             return self._run_evaluate()
         if self.predicting:
             return self._run_predict()
-        return self._run_train()
+        self._run_train()
 
-    def _pre_training_routine(self):
+    def _pre_training_routine(self) -> None:
         # wait for all to join if on distributed
         self.strategy.barrier("setup_training")
 
@@ -1147,6 +1157,7 @@ class Trainer:
             self._run_sanity_check()
 
         # enable train mode
+        assert self.model is not None
         self.model.train()
         torch.set_grad_enabled(True)
 
@@ -1229,6 +1240,7 @@ class Trainer:
             self.state.stage = stage
 
     def _call_setup_hook(self) -> None:
+        assert self.state.fn is not None
         fn = self.state.fn._setup_fn
 
         self.strategy.barrier("pre_setup")
@@ -1252,6 +1264,7 @@ class Trainer:
             self._call_callback_hooks("on_configure_sharded_model")
 
     def _call_teardown_hook(self) -> None:
+        assert self.state.fn is not None
         fn = self.state.fn._setup_fn
 
         if self.datamodule is not None:
@@ -1392,7 +1405,7 @@ class Trainer:
             prev_fx_name = pl_module._current_fx_name
             pl_module._current_fx_name = "on_load_checkpoint"
 
-        callback_states: Dict[Union[Type, str], Dict] = checkpoint.get("callbacks")
+        callback_states: Optional[Dict[Union[Type, str], Dict]] = checkpoint.get("callbacks")
 
         if callback_states is None:
             return
@@ -1420,7 +1433,7 @@ class Trainer:
 
     def _call_callbacks_load_state_dict(self, checkpoint: Dict[str, Any]) -> None:
         """Called when loading a model checkpoint, calls every callback's `load_state_dict`."""
-        callback_states: Dict[Union[Type, str], Dict] = checkpoint.get("callbacks")
+        callback_states: Optional[Dict[Union[Type, str], Dict]] = checkpoint.get("callbacks")
 
         if callback_states is None:
             return
@@ -1458,6 +1471,7 @@ class Trainer:
         torch._C._log_api_usage_once("lightning.trainer." + event)
 
     def __setup_profiler(self) -> None:
+        assert self.state.fn is not None
         local_rank = self.local_rank if self.world_size > 1 else None
         self.profiler._lightning_module = proxy(self.lightning_module)
         self.profiler.setup(stage=self.state.fn._setup_fn, local_rank=local_rank, log_dir=self.log_dir)
@@ -1516,7 +1530,7 @@ class Trainer:
 
         module = model or self.lightning_module or self.datamodule
         orig_train_batches = self.num_training_batches = (
-            len(self.train_dataloader)
+            len(self.train_dataloader)  # type: ignore[arg-type]
             if has_len_all_ranks(self.train_dataloader, self.strategy, module)
             else float("inf")
         )
@@ -1661,11 +1675,13 @@ class Trainer:
 
     @property
     def accelerator(self) -> Accelerator:
+        assert self.strategy.accelerator
         return self.strategy.accelerator
 
     @property
     def strategy(self) -> Strategy:
-        return self._accelerator_connector.strategy
+        # TODO(lite): remove ignore after merging lite and PL strategies
+        return self._accelerator_connector.strategy  # type: ignore[return-value]
 
     @property
     def precision_plugin(self) -> PrecisionPlugin:
@@ -1702,6 +1718,7 @@ class Trainer:
             if isinstance(self.strategy, ParallelStrategy)
             else [self.strategy.root_device]
         )
+        assert devices is not None
         device_ids = []
         for idx, device in enumerate(devices):
             if isinstance(device, torch.device):
@@ -1718,14 +1735,14 @@ class Trainer:
     @property
     def lightning_module(self) -> "pl.LightningModule":
         # TODO: this is actually an optional return
-        return self.strategy.lightning_module
+        return self.strategy.lightning_module  # type: ignore[return-value]
 
     @property
     def optimizers(self) -> List[Optimizer]:
         return self.strategy.optimizers
 
     @optimizers.setter
-    def optimizers(self, new_optims: Optional[List[Optimizer]]) -> None:
+    def optimizers(self, new_optims: List[Optimizer]) -> None:
         self.strategy.optimizers = new_optims
 
     @property
@@ -1757,7 +1774,7 @@ class Trainer:
         return getattr(self.precision_plugin, "scaler", None)
 
     @property
-    def model(self) -> torch.nn.Module:
+    def model(self) -> Optional[torch.nn.Module]:
         """The LightningModule, but possibly wrapped into DataParallel or DistributedDataParallel.
 
         To access the pure LightningModule, use
@@ -1783,10 +1800,10 @@ class Trainer:
     @property
     def log_dir(self) -> Optional[str]:
         if len(self.loggers) > 0:
-            if isinstance(self.loggers[0], TensorBoardLogger):
-                dirpath = self.loggers[0].log_dir
-            else:
+            if not isinstance(self.loggers[0], TensorBoardLogger):
                 dirpath = self.loggers[0].save_dir
+            else:
+                dirpath = self.loggers[0].log_dir
         else:
             dirpath = self.default_root_dir
 
@@ -1915,7 +1932,7 @@ class Trainer:
         return {k: v.default for k, v in init_signature.parameters.items()}
 
     @classmethod
-    def from_argparse_args(cls: Any, args: Union[Namespace, ArgumentParser], **kwargs) -> Any:
+    def from_argparse_args(cls: Any, args: Union[Namespace, ArgumentParser], **kwargs: Any) -> Any:
         return from_argparse_args(cls, args, **kwargs)
 
     @classmethod
@@ -1927,7 +1944,7 @@ class Trainer:
         return parse_env_variables(cls)
 
     @classmethod
-    def add_argparse_args(cls, parent_parser: ArgumentParser, **kwargs) -> ArgumentParser:
+    def add_argparse_args(cls, parent_parser: ArgumentParser, **kwargs: Any) -> Union[_ArgumentGroup, ArgumentParser]:
         return add_argparse_args(cls, parent_parser, **kwargs)
 
     """
@@ -1995,7 +2012,7 @@ class Trainer:
 
     @property
     def evaluating(self) -> bool:
-        return self.state.stage and self.state.stage.evaluating
+        return self.state.stage is not None and self.state.stage.evaluating
 
     @property
     def sanity_checking(self) -> bool:
@@ -2026,11 +2043,11 @@ class Trainer:
         return self.fit_loop.epoch_progress.current.completed
 
     @property
-    def max_epochs(self) -> int:
+    def max_epochs(self) -> Optional[int]:
         return self.fit_loop.max_epochs
 
     @property
-    def min_epochs(self) -> int:
+    def min_epochs(self) -> Optional[int]:
         return self.fit_loop.min_epochs
 
     @property
@@ -2051,7 +2068,7 @@ class Trainer:
         return self._fit_loop
 
     @fit_loop.setter
-    def fit_loop(self, loop: FitLoop):
+    def fit_loop(self, loop: FitLoop) -> None:
         """Attach a custom fit loop to this Trainer.
 
         It will run with
@@ -2065,7 +2082,7 @@ class Trainer:
         return self._validate_loop
 
     @validate_loop.setter
-    def validate_loop(self, loop: EvaluationLoop):
+    def validate_loop(self, loop: EvaluationLoop) -> None:
         """Attach a custom validation loop to this Trainer.
 
         It will run with
@@ -2080,7 +2097,7 @@ class Trainer:
         return self._test_loop
 
     @test_loop.setter
-    def test_loop(self, loop: EvaluationLoop):
+    def test_loop(self, loop: EvaluationLoop) -> None:
         """Attach a custom test loop to this Trainer.
 
         It will run with
@@ -2094,7 +2111,7 @@ class Trainer:
         return self._predict_loop
 
     @predict_loop.setter
-    def predict_loop(self, loop: PredictionLoop):
+    def predict_loop(self, loop: PredictionLoop) -> None:
         """Attach a custom prediction loop to this Trainer.
 
         It will run with
@@ -2146,17 +2163,17 @@ class Trainer:
         self._loggers = loggers if loggers else []
 
     @property
-    def callback_metrics(self) -> Dict[str, Tensor]:
+    def callback_metrics(self) -> Dict:
         # TODO: the true typing return can include dictionaries as defined in
         # `pytorch_lightning.trainer.connectors.logger_connector.result._OUT_DICT`
         return self._logger_connector.callback_metrics
 
     @property
-    def logged_metrics(self) -> dict:
+    def logged_metrics(self) -> _OUT_DICT:
         return self._logger_connector.logged_metrics
 
     @property
-    def progress_bar_metrics(self) -> dict:
+    def progress_bar_metrics(self) -> _PBAR_DICT:
         return self._logger_connector.progress_bar_metrics
 
     @property
@@ -2172,7 +2189,7 @@ class Trainer:
 
     def _should_terminate_gracefully(self) -> bool:
         value = torch.tensor(int(self._terminate_gracefully), device=self.strategy.root_device)
-        return self.strategy.reduce(value, reduce_op="sum") > 0
+        return bool(self.strategy.reduce(value, reduce_op="sum") > 0)
 
     """
     Other
@@ -2216,6 +2233,7 @@ class Trainer:
         if total_batches == float("inf"):
             return self.max_steps
 
+        assert self.max_epochs is not None
         self.accumulate_grad_batches = accumulation_scheduler.get_accumulate_grad_batches(self.current_epoch)
         effective_batch_size = self.accumulate_grad_batches
         max_estimated_steps = math.ceil(total_batches / effective_batch_size) * max(self.max_epochs, 1)
diff --git a/src/pytorch_lightning/tuner/batch_size_scaling.py b/src/pytorch_lightning/tuner/batch_size_scaling.py
index 781c7ee119..82ea298a6b 100644
--- a/src/pytorch_lightning/tuner/batch_size_scaling.py
+++ b/src/pytorch_lightning/tuner/batch_size_scaling.py
@@ -17,8 +17,6 @@ import uuid
 from copy import deepcopy
 from typing import Any, Dict, Optional, Tuple
 
-from torch.utils.data import DataLoader
-
 import pytorch_lightning as pl
 from pytorch_lightning.utilities.memory import garbage_collection_cuda, is_oom_error
 from pytorch_lightning.utilities.parsing import lightning_getattr, lightning_setattr
@@ -277,13 +275,15 @@ def _adjust_batch_size(
         rank_zero_info(f"Batch size {batch_size} {desc}, trying batch size {new_size}")
 
     if trainer.state.fn == "fit":
+        from pytorch_lightning.trainer.supporters import CombinedLoader
+
         if trainer.train_dataloader is None:
             trainer.reset_train_dataloader()
 
-        assert trainer.train_dataloader is not None
-        # TODO: should we check val_dataloaders here too?
+        assert isinstance(trainer.train_dataloader, CombinedLoader)
         if not _is_valid_batch_size(new_size, trainer.train_dataloader, trainer):
-            new_size = min(new_size, len(trainer.train_dataloader.dataset))
+            # at this moment, `train_dataloader` is already a CombinedLoader. len can return a size or infinity
+            new_size = min(new_size, len(trainer.train_dataloader.dataset))  # type: ignore[arg-type]
     else:
         stage = trainer.state.stage
         assert stage is not None
@@ -302,11 +302,14 @@ def _adjust_batch_size(
     return new_size, changed
 
 
-def _is_valid_batch_size(batch_size: int, dataloader: DataLoader, trainer: "pl.Trainer") -> bool:
+def _is_valid_batch_size(
+    batch_size: int, dataloader: "pl.trainer.supporters.CombinedLoader", trainer: "pl.Trainer"
+) -> bool:
     from pytorch_lightning.utilities.data import has_len_all_ranks
 
     module = trainer.lightning_module or trainer.datamodule
-    return not has_len_all_ranks(dataloader, trainer.strategy, module) or batch_size <= len(dataloader)
+    has_len = has_len_all_ranks(dataloader, trainer.strategy, module)
+    return not has_len or batch_size <= len(dataloader)  # type: ignore[arg-type]
 
 
 def _reset_dataloaders(trainer: "pl.Trainer", pl_module: "pl.LightningModule") -> None:
diff --git a/src/pytorch_lightning/utilities/data.py b/src/pytorch_lightning/utilities/data.py
index 17f8b9f101..e2efb4f562 100644
--- a/src/pytorch_lightning/utilities/data.py
+++ b/src/pytorch_lightning/utilities/data.py
@@ -35,6 +35,7 @@ from lightning_lite.utilities.data import has_iterable_dataset as new_has_iterab
 from lightning_lite.utilities.data import has_len as new_has_len
 from pytorch_lightning.overrides.distributed import IndexBatchSamplerWrapper
 from pytorch_lightning.trainer.states import RunningStage
+from pytorch_lightning.trainer.supporters import CombinedLoader
 from pytorch_lightning.utilities.auto_restart import CaptureIterableDataset, CaptureMapDataset, FastForwardSampler
 from pytorch_lightning.utilities.enums import _FaultTolerantMode
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
@@ -96,14 +97,14 @@ def extract_batch_size(batch: BType) -> int:
 
 
 def has_len_all_ranks(
-    dataloader: DataLoader,
+    dataloader: Union[DataLoader, CombinedLoader],
     strategy: "pl.strategies.Strategy",
     model: Union["pl.LightningModule", "pl.LightningDataModule"],
 ) -> bool:
     """Checks if a given Dataloader has ``__len__`` method implemented i.e. if it is a finite dataloader or
     infinite dataloader."""
     try:
-        local_length = len(dataloader)
+        local_length = len(dataloader)  # type: ignore [arg-type] # we are checking with duck-typing
         total_length = strategy.reduce(torch.tensor(local_length, device=strategy.root_device), reduce_op="sum")
 
         if total_length == 0:
@@ -129,7 +130,8 @@ def has_len_all_ranks(
     except (TypeError, NotImplementedError):
         has_len = False
 
-    if has_len and new_has_iterable_dataset(dataloader):
+    # we are checking using lightning_lite, which doesn't know CombinedLoader
+    if has_len and new_has_iterable_dataset(dataloader):  # type: ignore [arg-type]
         rank_zero_warn(
             "Your `IterableDataset` has `__len__` defined."
             " In combination with multi-process data loading (when num_workers > 1),"
diff --git a/src/pytorch_lightning/utilities/parsing.py b/src/pytorch_lightning/utilities/parsing.py
index 22dfb53882..87d43791e5 100644
--- a/src/pytorch_lightning/utilities/parsing.py
+++ b/src/pytorch_lightning/utilities/parsing.py
@@ -17,9 +17,8 @@ import copy
 import inspect
 import pickle
 import types
-from argparse import Namespace
 from dataclasses import fields, is_dataclass
-from typing import Any, Dict, List, Optional, Sequence, Tuple, Type, Union
+from typing import Any, Dict, List, MutableMapping, Optional, Sequence, Tuple, Type, Union
 
 from torch import nn
 from typing_extensions import Literal
@@ -94,18 +93,13 @@ def is_picklable(obj: object) -> bool:
         return False
 
 
-def clean_namespace(hparams: Union[Dict[str, Any], Namespace]) -> None:
+def clean_namespace(hparams: MutableMapping) -> None:
     """Removes all unpicklable entries from hparams."""
-
-    hparams_dict = hparams
-    if isinstance(hparams, Namespace):
-        hparams_dict = hparams.__dict__
-
-    del_attrs = [k for k, v in hparams_dict.items() if not is_picklable(v)]
+    del_attrs = [k for k, v in hparams.items() if not is_picklable(v)]
 
     for k in del_attrs:
         rank_zero_warn(f"attribute '{k}' removed from hparams because it cannot be pickled")
-        del hparams_dict[k]
+        del hparams[k]
 
 
 def parse_class_init_keys(