diff --git a/pandas/_libs/tslibs/offsets.pyi b/pandas/_libs/tslibs/offsets.pyi
index 12b113f0b73b1..4567dde4e056b 100644
--- a/pandas/_libs/tslibs/offsets.pyi
+++ b/pandas/_libs/tslibs/offsets.pyi
@@ -104,7 +104,9 @@ class SingleConstructorOffset(BaseOffset):
 @overload
 def to_offset(freq: None) -> None: ...
 @overload
-def to_offset(freq: timedelta | BaseOffset | str) -> BaseOffset: ...
+def to_offset(freq: _BaseOffsetT) -> _BaseOffsetT: ...
+@overload
+def to_offset(freq: timedelta | str) -> BaseOffset: ...
 
 class Tick(SingleConstructorOffset):
     _reso: int
diff --git a/pandas/compat/numpy/function.py b/pandas/compat/numpy/function.py
index e3aa5bb52f2ba..140d41782e6d3 100644
--- a/pandas/compat/numpy/function.py
+++ b/pandas/compat/numpy/function.py
@@ -17,7 +17,11 @@
 """
 from __future__ import annotations
 
-from typing import Any
+from typing import (
+    Any,
+    TypeVar,
+    overload,
+)
 
 from numpy import ndarray
 
@@ -25,6 +29,7 @@
     is_bool,
     is_integer,
 )
+from pandas._typing import Axis
 from pandas.errors import UnsupportedFunctionCall
 from pandas.util._validators import (
     validate_args,
@@ -32,6 +37,8 @@
     validate_kwargs,
 )
 
+AxisNoneT = TypeVar("AxisNoneT", Axis, None)
+
 
 class CompatValidator:
     def __init__(
@@ -84,7 +91,7 @@ def __call__(
 )
 
 
-def process_skipna(skipna, args):
+def process_skipna(skipna: bool | ndarray | None, args) -> tuple[bool, Any]:
     if isinstance(skipna, ndarray) or skipna is None:
         args = (skipna,) + args
         skipna = True
@@ -92,7 +99,7 @@ def process_skipna(skipna, args):
     return skipna, args
 
 
-def validate_argmin_with_skipna(skipna, args, kwargs):
+def validate_argmin_with_skipna(skipna: bool | ndarray | None, args, kwargs) -> bool:
     """
     If 'Series.argmin' is called via the 'numpy' library, the third parameter
     in its signature is 'out', which takes either an ndarray or 'None', so
@@ -104,7 +111,7 @@ def validate_argmin_with_skipna(skipna, args, kwargs):
     return skipna
 
 
-def validate_argmax_with_skipna(skipna, args, kwargs):
+def validate_argmax_with_skipna(skipna: bool | ndarray | None, args, kwargs) -> bool:
     """
     If 'Series.argmax' is called via the 'numpy' library, the third parameter
     in its signature is 'out', which takes either an ndarray or 'None', so
@@ -137,7 +144,7 @@ def validate_argmax_with_skipna(skipna, args, kwargs):
 )
 
 
-def validate_argsort_with_ascending(ascending, args, kwargs):
+def validate_argsort_with_ascending(ascending: bool | int | None, args, kwargs) -> bool:
     """
     If 'Categorical.argsort' is called via the 'numpy' library, the first
     parameter in its signature is 'axis', which takes either an integer or
@@ -149,7 +156,8 @@ def validate_argsort_with_ascending(ascending, args, kwargs):
         ascending = True
 
     validate_argsort_kind(args, kwargs, max_fname_arg_count=3)
-    return ascending
+    # error: Incompatible return value type (got "int", expected "bool")
+    return ascending  # type: ignore[return-value]
 
 
 CLIP_DEFAULTS: dict[str, Any] = {"out": None}
@@ -158,7 +166,19 @@ def validate_argsort_with_ascending(ascending, args, kwargs):
 )
 
 
-def validate_clip_with_axis(axis, args, kwargs):
+@overload
+def validate_clip_with_axis(axis: ndarray, args, kwargs) -> None:
+    ...
+
+
+@overload
+def validate_clip_with_axis(axis: AxisNoneT, args, kwargs) -> AxisNoneT:
+    ...
+
+
+def validate_clip_with_axis(
+    axis: ndarray | AxisNoneT, args, kwargs
+) -> AxisNoneT | None:
     """
     If 'NDFrame.clip' is called via the numpy library, the third parameter in
     its signature is 'out', which can takes an ndarray, so check if the 'axis'
@@ -167,10 +187,14 @@ def validate_clip_with_axis(axis, args, kwargs):
     """
     if isinstance(axis, ndarray):
         args = (axis,) + args
-        axis = None
+        # error: Incompatible types in assignment (expression has type "None",
+        # variable has type "Union[ndarray[Any, Any], str, int]")
+        axis = None  # type: ignore[assignment]
 
     validate_clip(args, kwargs)
-    return axis
+    # error: Incompatible return value type (got "Union[ndarray[Any, Any],
+    # str, int]", expected "Union[str, int, None]")
+    return axis  # type: ignore[return-value]
 
 
 CUM_FUNC_DEFAULTS: dict[str, Any] = {}
@@ -184,7 +208,7 @@ def validate_clip_with_axis(axis, args, kwargs):
 )
 
 
-def validate_cum_func_with_skipna(skipna, args, kwargs, name):
+def validate_cum_func_with_skipna(skipna, args, kwargs, name) -> bool:
     """
     If this function is called via the 'numpy' library, the third parameter in
     its signature is 'dtype', which takes either a 'numpy' dtype or 'None', so
@@ -288,7 +312,7 @@ def validate_cum_func_with_skipna(skipna, args, kwargs, name):
 validate_take = CompatValidator(TAKE_DEFAULTS, fname="take", method="kwargs")
 
 
-def validate_take_with_convert(convert, args, kwargs):
+def validate_take_with_convert(convert: ndarray | bool | None, args, kwargs) -> bool:
     """
     If this function is called via the 'numpy' library, the third parameter in
     its signature is 'axis', which takes either an ndarray or 'None', so check
diff --git a/pandas/core/arrays/datetimelike.py b/pandas/core/arrays/datetimelike.py
index 0f88ad9811bf0..325c94d0ea267 100644
--- a/pandas/core/arrays/datetimelike.py
+++ b/pandas/core/arrays/datetimelike.py
@@ -2164,7 +2164,17 @@ def ensure_arraylike_for_datetimelike(data, copy: bool, cls_name: str):
     return data, copy
 
 
-def validate_periods(periods):
+@overload
+def validate_periods(periods: None) -> None:
+    ...
+
+
+@overload
+def validate_periods(periods: int | float) -> int:
+    ...
+
+
+def validate_periods(periods: int | float | None) -> int | None:
     """
     If a `periods` argument is passed to the Datetime/Timedelta Array/Index
     constructor, cast it to an integer.
@@ -2187,7 +2197,9 @@ def validate_periods(periods):
             periods = int(periods)
         elif not lib.is_integer(periods):
             raise TypeError(f"periods must be a number, got {periods}")
-    return periods
+    # error: Incompatible return value type (got "Optional[float]",
+    # expected "Optional[int]")
+    return periods  # type: ignore[return-value]
 
 
 def validate_inferred_freq(freq, inferred_freq, freq_infer):
diff --git a/pandas/core/arrays/datetimes.py b/pandas/core/arrays/datetimes.py
index 106afcc3c12ea..d9f6cecc8d61d 100644
--- a/pandas/core/arrays/datetimes.py
+++ b/pandas/core/arrays/datetimes.py
@@ -251,7 +251,7 @@ def _scalar_type(self) -> type[Timestamp]:
     # Constructors
 
     _dtype: np.dtype | DatetimeTZDtype
-    _freq = None
+    _freq: BaseOffset | None = None
     _default_dtype = DT64NS_DTYPE  # used in TimeLikeOps.__init__
 
     @classmethod
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index fa7c4e0d0aa70..6e6de8399cc38 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -8,6 +8,8 @@
     Callable,
     Literal,
     Sequence,
+    TypeVar,
+    overload,
 )
 
 import numpy as np
@@ -92,6 +94,8 @@
         TimedeltaArray,
     )
 
+BaseOffsetT = TypeVar("BaseOffsetT", bound=BaseOffset)
+
 
 _shared_doc_kwargs = {
     "klass": "PeriodArray",
@@ -976,7 +980,19 @@ def period_array(
     return PeriodArray._from_sequence(data, dtype=dtype)
 
 
-def validate_dtype_freq(dtype, freq):
+@overload
+def validate_dtype_freq(dtype, freq: BaseOffsetT) -> BaseOffsetT:
+    ...
+
+
+@overload
+def validate_dtype_freq(dtype, freq: timedelta | str | None) -> BaseOffset:
+    ...
+
+
+def validate_dtype_freq(
+    dtype, freq: BaseOffsetT | timedelta | str | None
+) -> BaseOffsetT:
     """
     If both a dtype and a freq are available, ensure they match.  If only
     dtype is available, extract the implied freq.
@@ -996,7 +1012,10 @@ def validate_dtype_freq(dtype, freq):
     IncompatibleFrequency : mismatch between dtype and freq
     """
     if freq is not None:
-        freq = to_offset(freq)
+        # error: Incompatible types in assignment (expression has type
+        # "BaseOffset", variable has type "Union[BaseOffsetT, timedelta,
+        # str, None]")
+        freq = to_offset(freq)  # type: ignore[assignment]
 
     if dtype is not None:
         dtype = pandas_dtype(dtype)
@@ -1006,7 +1025,9 @@ def validate_dtype_freq(dtype, freq):
             freq = dtype.freq
         elif freq != dtype.freq:
             raise IncompatibleFrequency("specified freq and dtype are different")
-    return freq
+    # error: Incompatible return value type (got "Union[BaseOffset, Any, None]",
+    # expected "BaseOffset")
+    return freq  # type: ignore[return-value]
 
 
 def dt64arr_to_periodarr(
diff --git a/pandas/util/_validators.py b/pandas/util/_validators.py
index 3676e6eb0091e..fc3439a57a002 100644
--- a/pandas/util/_validators.py
+++ b/pandas/util/_validators.py
@@ -5,6 +5,7 @@
 from __future__ import annotations
 
 from typing import (
+    Any,
     Iterable,
     Sequence,
     TypeVar,
@@ -265,7 +266,9 @@ def validate_bool_kwarg(
     return value
 
 
-def validate_axis_style_args(data, args, kwargs, arg_name, method_name):
+def validate_axis_style_args(
+    data, args, kwargs, arg_name, method_name
+) -> dict[str, Any]:
     """
     Argument handler for mixed index, columns / axis functions