diff --git a/doc/source/whatsnew/v1.1.0.rst b/doc/source/whatsnew/v1.1.0.rst
index b05911a4d1eb0..eb18e1e07547b 100644
--- a/doc/source/whatsnew/v1.1.0.rst
+++ b/doc/source/whatsnew/v1.1.0.rst
@@ -444,6 +444,8 @@ Groupby/resample/rolling
 - Bug in :meth:`DataFrameGroupby.transform` produces incorrect result with transformation functions (:issue:`30918`)
 - Bug in :meth:`GroupBy.count` causes segmentation fault when grouped-by column contains NaNs (:issue:`32841`)
 - Bug in :meth:`DataFrame.groupby` and :meth:`Series.groupby` produces inconsistent type when aggregating Boolean series (:issue:`32894`)
+- Bug in :meth:`SeriesGroupBy.first`, :meth:`SeriesGroupBy.last`, :meth:`SeriesGroupBy.min`, and :meth:`SeriesGroupBy.max` returning floats when applied to nullable Booleans (:issue:`33071`)
+- Bug in :meth:`DataFrameGroupBy.agg` with dictionary input losing ``ExtensionArray`` dtypes (:issue:`32194`)
 - Bug in :meth:`DataFrame.resample` where an ``AmbiguousTimeError`` would be raised when the resulting timezone aware :class:`DatetimeIndex` had a DST transition at midnight (:issue:`25758`)
 
 Reshaping
diff --git a/pandas/core/dtypes/cast.py b/pandas/core/dtypes/cast.py
index 223cc43d158e6..7dda6850ba4f7 100644
--- a/pandas/core/dtypes/cast.py
+++ b/pandas/core/dtypes/cast.py
@@ -33,6 +33,7 @@
     ensure_str,
     is_bool,
     is_bool_dtype,
+    is_categorical_dtype,
     is_complex,
     is_complex_dtype,
     is_datetime64_dtype,
@@ -279,12 +280,15 @@ def maybe_cast_result(result, obj: "Series", numeric_only: bool = False, how: st
     dtype = maybe_cast_result_dtype(dtype, how)
 
     if not is_scalar(result):
-        if is_extension_array_dtype(dtype) and dtype.kind != "M":
-            # The result may be of any type, cast back to original
-            # type if it's compatible.
-            if len(result) and isinstance(result[0], dtype.type):
-                cls = dtype.construct_array_type()
-                result = maybe_cast_to_extension_array(cls, result, dtype=dtype)
+        if (
+            is_extension_array_dtype(dtype)
+            and not is_categorical_dtype(dtype)
+            and dtype.kind != "M"
+        ):
+            # We have to special case categorical so as not to upcast
+            # things like counts back to categorical
+            cls = dtype.construct_array_type()
+            result = maybe_cast_to_extension_array(cls, result, dtype=dtype)
 
         elif numeric_only and is_numeric_dtype(dtype) or not numeric_only:
             result = maybe_downcast_to_dtype(result, dtype)
diff --git a/pandas/tests/groupby/test_nth.py b/pandas/tests/groupby/test_nth.py
index b1476f1059d84..e1bc058508bee 100644
--- a/pandas/tests/groupby/test_nth.py
+++ b/pandas/tests/groupby/test_nth.py
@@ -384,6 +384,32 @@ def test_first_last_tz_multi_column(method, ts, alpha):
     tm.assert_frame_equal(result, expected)
 
 
+@pytest.mark.parametrize(
+    "values",
+    [
+        pd.array([True, False], dtype="boolean"),
+        pd.array([1, 2], dtype="Int64"),
+        pd.to_datetime(["2020-01-01", "2020-02-01"]),
+        pd.to_timedelta([1, 2], unit="D"),
+    ],
+)
+@pytest.mark.parametrize("function", ["first", "last", "min", "max"])
+def test_first_last_extension_array_keeps_dtype(values, function):
+    # https://github.com/pandas-dev/pandas/issues/33071
+    # https://github.com/pandas-dev/pandas/issues/32194
+    df = DataFrame({"a": [1, 2], "b": values})
+    grouped = df.groupby("a")
+    idx = Index([1, 2], name="a")
+    expected_series = Series(values, name="b", index=idx)
+    expected_frame = DataFrame({"b": values}, index=idx)
+
+    result_series = getattr(grouped["b"], function)()
+    tm.assert_series_equal(result_series, expected_series)
+
+    result_frame = grouped.agg({"b": function})
+    tm.assert_frame_equal(result_frame, expected_frame)
+
+
 def test_nth_multi_index_as_expected():
     # PR 9090, related to issue 8979
     # test nth on MultiIndex
diff --git a/pandas/tests/resample/test_datetime_index.py b/pandas/tests/resample/test_datetime_index.py
index bbb294bc109c1..f15d39e9e6456 100644
--- a/pandas/tests/resample/test_datetime_index.py
+++ b/pandas/tests/resample/test_datetime_index.py
@@ -122,9 +122,7 @@ def test_resample_integerarray():
 
     result = ts.resample("3T").mean()
     expected = Series(
-        [1, 4, 7],
-        index=pd.date_range("1/1/2000", periods=3, freq="3T"),
-        dtype="float64",
+        [1, 4, 7], index=pd.date_range("1/1/2000", periods=3, freq="3T"), dtype="Int64",
     )
     tm.assert_series_equal(result, expected)