diff --git a/pandas/core/arrays/_mixins.py b/pandas/core/arrays/_mixins.py
index 948ffdc1f7c01..726ca0ce4d776 100644
--- a/pandas/core/arrays/_mixins.py
+++ b/pandas/core/arrays/_mixins.py
@@ -233,6 +233,9 @@ def fillna(self: _T, value=None, method=None, limit=None) -> _T:
             new_values = self.copy()
         return new_values
 
+    # ------------------------------------------------------------------------
+    # Reductions
+
     def _reduce(self, name: str, skipna: bool = True, **kwargs):
         meth = getattr(self, name, None)
         if meth:
diff --git a/pandas/core/arrays/period.py b/pandas/core/arrays/period.py
index ef8093660b413..b95a7acc19b1f 100644
--- a/pandas/core/arrays/period.py
+++ b/pandas/core/arrays/period.py
@@ -207,8 +207,6 @@ def _from_sequence(
             return scalars
 
         periods = np.asarray(scalars, dtype=object)
-        if copy:
-            periods = periods.copy()
 
         freq = freq or libperiod.extract_freq(periods)
         ordinals = libperiod.extract_ordinals(periods, freq)
diff --git a/pandas/core/arrays/timedeltas.py b/pandas/core/arrays/timedeltas.py
index 17fcd00b7b251..c948291f29aeb 100644
--- a/pandas/core/arrays/timedeltas.py
+++ b/pandas/core/arrays/timedeltas.py
@@ -120,7 +120,7 @@ class TimedeltaArray(dtl.TimelikeOps):
         "ceil",
     ]
 
-    # Note: ndim must be defined to ensure NaT.__richcmp(TimedeltaArray)
+    # Note: ndim must be defined to ensure NaT.__richcmp__(TimedeltaArray)
     #  operates pointwise.
 
     def _box_func(self, x) -> Union[Timedelta, NaTType]:
@@ -520,7 +520,7 @@ def __mul__(self, other) -> "TimedeltaArray":
     def __truediv__(self, other):
         # timedelta / X is well-defined for timedelta-like or numeric X
 
-        if isinstance(other, (timedelta, np.timedelta64, Tick)):
+        if isinstance(other, self._recognized_scalars):
             other = Timedelta(other)
             if other is NaT:
                 # specifically timedelta64-NaT
@@ -577,7 +577,7 @@ def __truediv__(self, other):
     @unpack_zerodim_and_defer("__rtruediv__")
     def __rtruediv__(self, other):
         # X / timedelta is defined only for timedelta-like X
-        if isinstance(other, (timedelta, np.timedelta64, Tick)):
+        if isinstance(other, self._recognized_scalars):
             other = Timedelta(other)
             if other is NaT:
                 # specifically timedelta64-NaT
@@ -620,7 +620,7 @@ def __rtruediv__(self, other):
     def __floordiv__(self, other):
 
         if is_scalar(other):
-            if isinstance(other, (timedelta, np.timedelta64, Tick)):
+            if isinstance(other, self._recognized_scalars):
                 other = Timedelta(other)
                 if other is NaT:
                     # treat this specifically as timedelta-NaT
@@ -684,7 +684,7 @@ def __floordiv__(self, other):
     def __rfloordiv__(self, other):
 
         if is_scalar(other):
-            if isinstance(other, (timedelta, np.timedelta64, Tick)):
+            if isinstance(other, self._recognized_scalars):
                 other = Timedelta(other)
                 if other is NaT:
                     # treat this specifically as timedelta-NaT
@@ -730,21 +730,21 @@ def __rfloordiv__(self, other):
     @unpack_zerodim_and_defer("__mod__")
     def __mod__(self, other):
         # Note: This is a naive implementation, can likely be optimized
-        if isinstance(other, (timedelta, np.timedelta64, Tick)):
+        if isinstance(other, self._recognized_scalars):
             other = Timedelta(other)
         return self - (self // other) * other
 
     @unpack_zerodim_and_defer("__rmod__")
     def __rmod__(self, other):
         # Note: This is a naive implementation, can likely be optimized
-        if isinstance(other, (timedelta, np.timedelta64, Tick)):
+        if isinstance(other, self._recognized_scalars):
             other = Timedelta(other)
         return other - (other // self) * self
 
     @unpack_zerodim_and_defer("__divmod__")
     def __divmod__(self, other):
         # Note: This is a naive implementation, can likely be optimized
-        if isinstance(other, (timedelta, np.timedelta64, Tick)):
+        if isinstance(other, self._recognized_scalars):
             other = Timedelta(other)
 
         res1 = self // other
@@ -754,7 +754,7 @@ def __divmod__(self, other):
     @unpack_zerodim_and_defer("__rdivmod__")
     def __rdivmod__(self, other):
         # Note: This is a naive implementation, can likely be optimized
-        if isinstance(other, (timedelta, np.timedelta64, Tick)):
+        if isinstance(other, self._recognized_scalars):
             other = Timedelta(other)
 
         res1 = other // self
diff --git a/pandas/core/indexes/category.py b/pandas/core/indexes/category.py
index 6b64fd6a20e9a..fb0e710921a5f 100644
--- a/pandas/core/indexes/category.py
+++ b/pandas/core/indexes/category.py
@@ -578,7 +578,7 @@ def _convert_list_indexer(self, keyarr):
         return self.get_indexer(keyarr)
 
     @doc(Index._maybe_cast_slice_bound)
-    def _maybe_cast_slice_bound(self, label, side, kind):
+    def _maybe_cast_slice_bound(self, label, side: str, kind):
         if kind == "loc":
             return label
 
diff --git a/pandas/core/indexes/interval.py b/pandas/core/indexes/interval.py
index d8fab1283dfdc..7f0dc2426eba7 100644
--- a/pandas/core/indexes/interval.py
+++ b/pandas/core/indexes/interval.py
@@ -831,7 +831,7 @@ def _should_fallback_to_positional(self) -> bool:
         #  positional in this case
         return self.dtype.subtype.kind in ["m", "M"]
 
-    def _maybe_cast_slice_bound(self, label, side, kind):
+    def _maybe_cast_slice_bound(self, label, side: str, kind):
         return getattr(self, side)._maybe_cast_slice_bound(label, side, kind)
 
     @Appender(Index._convert_list_indexer.__doc__)
diff --git a/pandas/core/indexes/numeric.py b/pandas/core/indexes/numeric.py
index facaae3a65f16..546b90249b5ca 100644
--- a/pandas/core/indexes/numeric.py
+++ b/pandas/core/indexes/numeric.py
@@ -96,7 +96,7 @@ def _validate_dtype(cls, dtype: Dtype) -> None:
     # Indexing Methods
 
     @doc(Index._maybe_cast_slice_bound)
-    def _maybe_cast_slice_bound(self, label, side, kind):
+    def _maybe_cast_slice_bound(self, label, side: str, kind):
         assert kind in ["loc", "getitem", None]
 
         # we will try to coerce to integers
diff --git a/pandas/core/indexes/timedeltas.py b/pandas/core/indexes/timedeltas.py
index 302fead8c8b0c..66fd6943de721 100644
--- a/pandas/core/indexes/timedeltas.py
+++ b/pandas/core/indexes/timedeltas.py
@@ -8,8 +8,6 @@
 
 from pandas.core.dtypes.common import (
     TD64NS_DTYPE,
-    is_float,
-    is_integer,
     is_scalar,
     is_timedelta64_dtype,
     is_timedelta64_ns_dtype,
@@ -246,7 +244,7 @@ def _maybe_cast_slice_bound(self, label, side: str, kind):
                 return lbound
             else:
                 return lbound + to_offset(parsed.resolution_string) - Timedelta(1, "ns")
-        elif is_integer(label) or is_float(label):
+        elif not isinstance(label, self._data._recognized_scalars):
             self._invalid_indexer("slice", label)
 
         return label
diff --git a/pandas/core/sorting.py b/pandas/core/sorting.py
index 1132234ae7f8d..2e32a7572adc7 100644
--- a/pandas/core/sorting.py
+++ b/pandas/core/sorting.py
@@ -29,6 +29,7 @@
 from pandas.core.construction import extract_array
 
 if TYPE_CHECKING:
+    from pandas import MultiIndex
     from pandas.core.indexes.base import Index
 
 _INT64_MAX = np.iinfo(np.int64).max
@@ -415,7 +416,9 @@ def nargminmax(values, method: str):
     return non_nan_idx[func(non_nans)]
 
 
-def ensure_key_mapped_multiindex(index, key: Callable, level=None):
+def _ensure_key_mapped_multiindex(
+    index: "MultiIndex", key: Callable, level=None
+) -> "MultiIndex":
     """
     Returns a new MultiIndex in which key has been applied
     to all levels specified in level (or all levels if level
@@ -441,7 +444,6 @@ def ensure_key_mapped_multiindex(index, key: Callable, level=None):
     labels : MultiIndex
         Resulting MultiIndex with modified levels.
     """
-    from pandas.core.indexes.api import MultiIndex
 
     if level is not None:
         if isinstance(level, (str, int)):
@@ -460,7 +462,7 @@ def ensure_key_mapped_multiindex(index, key: Callable, level=None):
         for level in range(index.nlevels)
     ]
 
-    labels = MultiIndex.from_arrays(mapped)
+    labels = type(index).from_arrays(mapped)
 
     return labels
 
@@ -484,7 +486,7 @@ def ensure_key_mapped(values, key: Optional[Callable], levels=None):
         return values
 
     if isinstance(values, ABCMultiIndex):
-        return ensure_key_mapped_multiindex(values, key, level=levels)
+        return _ensure_key_mapped_multiindex(values, key, level=levels)
 
     result = key(values.copy())
     if len(result) != len(values):
diff --git a/pandas/tests/groupby/test_apply.py b/pandas/tests/groupby/test_apply.py
index f5078930a7b4b..a7c22b4983ed7 100644
--- a/pandas/tests/groupby/test_apply.py
+++ b/pandas/tests/groupby/test_apply.py
@@ -981,25 +981,6 @@ def test_apply_function_index_return(function):
     tm.assert_series_equal(result, expected)
 
 
-def test_apply_function_with_indexing():
-    # GH: 33058
-    df = DataFrame({"col1": ["A", "A", "A", "B", "B", "B"], "col2": [1, 2, 3, 4, 5, 6]})
-
-    def fn(x):
-        x.col2[x.index[-1]] = 0
-        return x.col2
-
-    result = df.groupby(["col1"], as_index=False).apply(fn)
-    expected = Series(
-        [1, 2, 0, 4, 5, 0],
-        index=pd.MultiIndex.from_tuples(
-            [(0, 0), (0, 1), (0, 2), (1, 3), (1, 4), (1, 5)]
-        ),
-        name="col2",
-    )
-    tm.assert_series_equal(result, expected)
-
-
 def test_apply_function_with_indexing_return_column():
     # GH: 7002
     df = DataFrame(