diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 7dcb950d279fe..92c10df3e4e97 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -169,6 +169,7 @@ jobs:
         pytest pandas/tests/indexing/multiindex/test_setitem.py::TestMultiIndexSetItem::test_frame_setitem_multi_column
 
         pytest pandas/tests/api/
+        pytest pandas/tests/apply/
         pytest pandas/tests/arrays/
         pytest pandas/tests/base/
         pytest pandas/tests/computation/
diff --git a/pandas/core/internals/array_manager.py b/pandas/core/internals/array_manager.py
index 1dae3d586a0a9..2177839eb34ce 100644
--- a/pandas/core/internals/array_manager.py
+++ b/pandas/core/internals/array_manager.py
@@ -929,6 +929,7 @@ def insert(self, loc: int, item: Hashable, value, allow_duplicates: bool = False
                 raise ValueError(
                     f"Expected a 1D array, got an array with shape {value.shape}"
                 )
+        value = ensure_wrapped_if_datetimelike(value)
 
         # TODO self.arrays can be empty
         # assert len(value) == len(self.arrays[0])
diff --git a/pandas/tests/apply/test_frame_apply.py b/pandas/tests/apply/test_frame_apply.py
index 8cebe1a888b77..227037ecba664 100644
--- a/pandas/tests/apply/test_frame_apply.py
+++ b/pandas/tests/apply/test_frame_apply.py
@@ -1435,9 +1435,10 @@ def test_apply_dtype(col):
     tm.assert_series_equal(result, expected)
 
 
-def test_apply_mutating():
+def test_apply_mutating(using_array_manager):
     # GH#35462 case where applied func pins a new BlockManager to a row
     df = DataFrame({"a": range(100), "b": range(100, 200)})
+    df_orig = df.copy()
 
     def func(row):
         mgr = row._mgr
@@ -1451,7 +1452,12 @@ def func(row):
     result = df.apply(func, axis=1)
 
     tm.assert_frame_equal(result, expected)
-    tm.assert_frame_equal(df, result)
+    if not using_array_manager:
+        # INFO(ArrayManager) With BlockManager, the row is a view and mutated in place,
+        # with ArrayManager the row is not a view, and thus not mutated in place
+        tm.assert_frame_equal(df, result)
+    else:
+        tm.assert_frame_equal(df, df_orig)
 
 
 def test_apply_empty_list_reduce():
diff --git a/pandas/tests/apply/test_frame_transform.py b/pandas/tests/apply/test_frame_transform.py
index 212a54b78dead..1a12cbff47092 100644
--- a/pandas/tests/apply/test_frame_transform.py
+++ b/pandas/tests/apply/test_frame_transform.py
@@ -39,8 +39,15 @@ def test_transform_ufunc(axis, float_frame, frame_or_series):
 
 
 @pytest.mark.parametrize("op", frame_transform_kernels)
-def test_transform_groupby_kernel(axis, float_frame, op):
+def test_transform_groupby_kernel(axis, float_frame, op, using_array_manager, request):
     # GH 35964
+    if using_array_manager and op == "pct_change" and axis in (1, "columns"):
+        # TODO(ArrayManager) shift with axis=1
+        request.node.add_marker(
+            pytest.mark.xfail(
+                reason="shift axis=1 not yet implemented for ArrayManager"
+            )
+        )
 
     args = [0.0] if op == "fillna" else []
     if axis == 0 or axis == "index":
diff --git a/pandas/tests/groupby/test_groupby.py b/pandas/tests/groupby/test_groupby.py
index afde1daca74c1..12247e2445295 100644
--- a/pandas/tests/groupby/test_groupby.py
+++ b/pandas/tests/groupby/test_groupby.py
@@ -840,7 +840,12 @@ def test_omit_nuisance(df):
 
     # won't work with axis = 1
     grouped = df.groupby({"A": 0, "C": 0, "D": 1, "E": 1}, axis=1)
-    msg = "reduction operation 'sum' not allowed for this dtype"
+    msg = "|".join(
+        [
+            "reduction operation 'sum' not allowed for this dtype",
+            "'DatetimeArray' does not implement reduction 'sum'",
+        ]
+    )
     with pytest.raises(TypeError, match=msg):
         grouped.agg(lambda x: x.sum(0, numeric_only=False))