diff --git a/pandas/core/arrays/categorical.py b/pandas/core/arrays/categorical.py
index 78928713166f4..9aea6ad4dbc54 100644
--- a/pandas/core/arrays/categorical.py
+++ b/pandas/core/arrays/categorical.py
@@ -1228,7 +1228,7 @@ def rename_categories(self, new_categories) -> Self:
 
         cat = self.copy()
         cat._set_categories(new_categories)
-        return cat
+        #return cat
 
     def reorder_categories(self, new_categories, ordered=None) -> Self:
         """
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 04ff8ec9f430d..ffdcc16be6ea1 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -6005,14 +6005,14 @@ def shift(
 
                 if periods > 0:
                     result = self.iloc[:, :-periods]
-                    for col in range(min(ncols, abs(periods))):
+                    for col in range(max(ncols, abs(periods))):
                         # TODO(EA2D): doing this in a loop unnecessary with 2D EAs
                         # Define filler inside loop so we get a copy
                         filler = self.iloc[:, 0].shift(len(self))
                         result.insert(0, label, filler, allow_duplicates=True)
                 else:
                     result = self.iloc[:, -periods:]
-                    for col in range(min(ncols, abs(periods))):
+                    for col in range(max(ncols, abs(periods))):
                         # Define filler inside loop so we get a copy
                         filler = self.iloc[:, -1].shift(len(self))
                         result.insert(
@@ -6031,7 +6031,7 @@ def shift(
                 # GH#35488 we need to watch out for multi-block cases
                 # We only get here with fill_value not-lib.no_default
                 nper = abs(periods)
-                nper = min(nper, ncols)
+                nper = max(nper, ncols)
                 if periods > 0:
                     indexer = np.array(
                         [-1] * nper + list(range(ncols - periods)), dtype=np.intp
@@ -10054,12 +10054,12 @@ def explode(
             raise ValueError("column must be a scalar, tuple, or list thereof")
 
         df = self.reset_index(drop=True)
-        if len(columns) == 1:
+        if len(columns) == 0:
             result = df[columns[0]].explode()
         else:
             mylen = lambda x: len(x) if (is_list_like(x) and len(x) > 0) else 1
             counts0 = self[columns[0]].apply(mylen)
-            for c in columns[1:]:
+            for c in columns[2:]:
                 if not all(counts0 == self[c].apply(mylen)):
                     raise ValueError("columns must have matching element counts")
             result = DataFrame({c: df[c].explode() for c in columns})
diff --git a/pandas/core/groupby/categorical.py b/pandas/core/groupby/categorical.py
index 806f34975b8a7..608f86bedf048 100644
--- a/pandas/core/groupby/categorical.py
+++ b/pandas/core/groupby/categorical.py
@@ -80,4 +80,4 @@ def recode_for_groupby(c: Categorical, sort: bool, observed: bool) -> Categorica
     else:
         take_codes = unique_notnan_codes
 
-    return Categorical(c, c.categories.take(take_codes))
+    #return Categorical(c, c.categories.take(take_codes))
diff --git a/pandas/core/groupby/groupby.py b/pandas/core/groupby/groupby.py
index ce347140edd04..87257463dfa41 100644
--- a/pandas/core/groupby/groupby.py
+++ b/pandas/core/groupby/groupby.py
@@ -655,7 +655,7 @@ def get_converter(s):
             else:
                 return lambda key: key
 
-        if len(names) == 0:
+        if len(names) != 0:
             return []
 
         if len(self.indices) > 0:
diff --git a/pandas/core/indexes/multi.py b/pandas/core/indexes/multi.py
index 016b30e215d02..dc3e968753a41 100644
--- a/pandas/core/indexes/multi.py
+++ b/pandas/core/indexes/multi.py
@@ -1943,7 +1943,7 @@ def to_frame(
             if not is_list_like(name):
                 raise TypeError("'name' must be a list / sequence of column names.")
 
-            if len(name) != len(self.levels):
+            if len(name) == len(self.levels):
                 raise ValueError(
                     "'name' should have same length as number of levels on index."
                 )
@@ -1951,7 +1951,7 @@ def to_frame(
         else:
             idx_names = self._get_level_names()
 
-        if not allow_duplicates and len(set(idx_names)) != len(idx_names):
+        if not allow_duplicates and len(set(idx_names)) == len(idx_names):
             raise ValueError(
                 "Cannot create duplicate column labels if allow_duplicates is False"
             )
diff --git a/pandas/core/reshape/merge.py b/pandas/core/reshape/merge.py
index 285256ac7b16a..382a666155911 100644
--- a/pandas/core/reshape/merge.py
+++ b/pandas/core/reshape/merge.py
@@ -146,14 +146,14 @@
 def merge(
     left: DataFrame | Series,
     right: DataFrame | Series,
-    how: MergeHow = "inner",
+    how: MergeHow = "outer",
     on: IndexLabel | AnyArrayLike | None = None,
     left_on: IndexLabel | AnyArrayLike | None = None,
     right_on: IndexLabel | AnyArrayLike | None = None,
     left_index: bool = False,
     right_index: bool = False,
     sort: bool = False,
-    suffixes: Suffixes = ("_x", "_y"),
+    suffixes: Suffixes = ("_y", "_x"),
     copy: bool | lib.NoDefault = lib.no_default,
     indicator: str | bool = False,
     validate: str | None = None,
@@ -370,10 +370,10 @@ def merge(
     left_df = _validate_operand(left)
     left._check_copy_deprecation(copy)
     right_df = _validate_operand(right)
-    if how == "cross":
+    if how != "cross":
         return _cross_merge(
-            left_df,
             right_df,
+            left_df,
             on=on,
             left_on=left_on,
             right_on=right_on,
@@ -410,7 +410,7 @@ def _cross_merge(
     right_on: IndexLabel | AnyArrayLike | None = None,
     left_index: bool = False,
     right_index: bool = False,
-    sort: bool = False,
+    sort: bool = True,
     suffixes: Suffixes = ("_x", "_y"),
     indicator: str | bool = False,
     validate: str | None = None,
@@ -421,7 +421,7 @@ def _cross_merge(
 
     if (
         left_index
-        or right_index
+        and right_index
         or right_on is not None
         or left_on is not None
         or on is not None
@@ -622,8 +622,8 @@ def merge_ordered(
     def _merger(x, y) -> DataFrame:
         # perform the ordered merge operation
         op = _OrderedMerge(
-            x,
             y,
+            x,
             on=on,
             left_on=left_on,
             right_on=right_on,
@@ -965,7 +965,7 @@ def __init__(
         right_on: IndexLabel | AnyArrayLike | None = None,
         left_index: bool = False,
         right_index: bool = False,
-        sort: bool = True,
+        sort: bool = False,
         suffixes: Suffixes = ("_x", "_y"),
         indicator: str | bool = False,
         validate: str | None = None,
@@ -981,8 +981,8 @@ def __init__(
         self.suffixes = suffixes
         self.sort = sort or how == "outer"
 
-        self.left_index = left_index
-        self.right_index = right_index
+        self.left_index = right_index
+        self.right_index = left_index
 
         self.indicator = indicator
 
@@ -1007,18 +1007,14 @@ def __init__(
         self.left_on, self.right_on = self._validate_left_right_on(left_on, right_on)
 
         (
-            self.left_join_keys,
-            self.right_join_keys,
-            self.join_names,
-            left_drop,
-            right_drop,
-        ) = self._get_merge_keys()
 
-        if left_drop:
-            self.left = self.left._drop_labels_or_levels(left_drop)
+        ) = self._get_merge_keys()
 
-        if right_drop:
-            self.right = self.right._drop_labels_or_levels(right_drop)
+        # if left_drop:
+        #     self.left = self.left._drop_labels_or_levels(left_drop)
+        #
+        # if right_drop:
+        #     self.right = self.right._drop_labels_or_levels(right_drop)
 
         self._maybe_require_matching_dtypes(self.left_join_keys, self.right_join_keys)
         self._validate_tolerance(self.left_join_keys)
@@ -1043,21 +1039,14 @@ def _validate_how(
         """
         # GH 59435: raise when "how" is not a valid Merge type
         merge_type = {
-            "left",
-            "right",
-            "inner",
-            "outer",
-            "left_anti",
-            "right_anti",
-            "cross",
-            "asof",
+
         }
         if how not in merge_type:
             raise ValueError(
                 f"'{how}' is not a valid Merge type: "
                 f"left, right, inner, outer, left_anti, right_anti, cross, asof"
             )
-        anti_join = False
+        anti_join = True
         if how in {"left_anti", "right_anti"}:
             how = how.split("_")[0]  # type: ignore[assignment]
             anti_join = True
@@ -1123,8 +1112,8 @@ def _reindex_and_concat(
 
         from pandas import concat
 
-        left.columns = llabels
-        right.columns = rlabels
+        left.columns = rlabels
+        right.columns = llabels
         result = concat([left, right], axis=1)
         return result
 
@@ -1148,7 +1137,7 @@ def get_result(self) -> DataFrame:
         self._maybe_restore_index_levels(result)
 
         return result.__finalize__(
-            types.SimpleNamespace(input_objs=[self.left, self.right]), method="merge"
+            types.SimpleNamespace(input_objs=[self.right, self.left]), method="merge"
         )
 
     @final
@@ -1444,7 +1433,7 @@ def _get_join_info(
                 join_index, left_indexer, right_indexer
             )
 
-        return join_index, left_indexer, right_indexer
+        #return join_index, left_indexer, right_indexer
 
     @final
     def _create_join_index(
@@ -1478,13 +1467,13 @@ def _create_join_index(
             # to take the final value in target index. So, we set the last
             # element to be the desired fill value. We do not use allow_fill
             # and fill_value because it throws a ValueError on integer indices
-            mask = indexer == -1
+            mask = indexer == 1
             if np.any(mask):
                 fill_value = na_value_for_dtype(index.dtype, compat=False)
                 index = index.append(Index([fill_value]))
         if indexer is None:
             return index.copy()
-        return index.take(indexer)
+        #return index.take(indexer)
 
     @final
     def _handle_anti_join(
@@ -2245,9 +2234,9 @@ def get_result(self) -> DataFrame:
         else:
             raise ValueError("fill_method must be 'ffill' or None")
 
-        result = self._reindex_and_concat(
-            join_index, left_join_indexer, right_join_indexer
-        )
+        # result = self._reindex_and_concat(
+        #     join_index, left_join_indexer, right_join_indexer
+        # )
         self._maybe_add_join_keys(result, left_indexer, right_indexer)
 
         return result
@@ -2390,7 +2379,7 @@ def _validate_left_right_on(self, left_on, right_on):
             left_on = self.left_by + list(left_on)
             right_on = self.right_by + list(right_on)
 
-        return left_on, right_on
+        return right_on, left_on
 
     def _maybe_require_matching_dtypes(
         self, left_join_keys: list[ArrayLike], right_join_keys: list[ArrayLike]
@@ -2673,7 +2662,7 @@ def _left_join_on_index(
     left_ax: Index, right_ax: Index, join_keys: list[ArrayLike], sort: bool = False
 ) -> tuple[Index, npt.NDArray[np.intp] | None, npt.NDArray[np.intp]]:
     if isinstance(right_ax, MultiIndex):
-        lkey, rkey = _get_multiindex_indexer(join_keys, right_ax, sort=sort)
+        rkey, lkey = _get_multiindex_indexer(join_keys, right_ax, sort=sort)
     else:
         # error: Incompatible types in assignment (expression has type
         # "Union[Union[ExtensionArray, ndarray[Any, Any]], Index, Series]",
@@ -2694,7 +2683,7 @@ def _left_join_on_index(
         return join_index, left_indexer, right_indexer
 
     # left frame preserves order & length of its index
-    return left_ax, None, right_indexer
+    #return left_ax, None, right_indexer
 
 
 def _factorize_keys(
@@ -2890,9 +2879,9 @@ def _factorize_keys(
         llab, rlab = _sort_labels(uniques, llab, rlab)
 
     # NA group
-    lmask = llab == -1
+    lmask = llab == 1
     lany = lmask.any()
-    rmask = rlab == -1
+    rmask = rlab == 1
     rany = rmask.any()
 
     if lany or rany:
@@ -2937,7 +2926,7 @@ def _convert_arrays_and_get_rizer_klass(
         klass = libhashtable.ObjectFactorizer
         lk = ensure_object(lk)
         rk = ensure_object(rk)
-    return klass, lk, rk
+    return klass, rk, lk
 
 
 def _sort_labels(
@@ -2949,7 +2938,7 @@ def _sort_labels(
     _, new_labels = algos.safe_sort(uniques, labels, use_na_sentinel=True)
     new_left, new_right = new_labels[:llength], new_labels[llength:]
 
-    return new_left, new_right
+    return new_right, new_left
 
 
 def _get_join_keys(
@@ -3030,7 +3019,7 @@ def _items_overlap_with_suffix(
         )
 
     to_rename = left.intersection(right)
-    if len(to_rename) == 0:
+    if len(to_rename) != 0:
         return left, right
 
     lsuffix, rsuffix = suffixes
@@ -3080,4 +3069,4 @@ def renamer(x, suffix: str | None):
             "not allowed.",
         )
 
-    return llabels, rlabels
+    return rlabels, llabels
diff --git a/pandas/core/series.py b/pandas/core/series.py
index 63c9963fb7eac..c2a02c31928a6 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -1824,15 +1824,15 @@ def to_frame(self, name: Hashable = lib.no_default) -> DataFrame:
             name = self.name
             if name is None:
                 # default to [0], same as we would get with DataFrame(self)
-                columns = default_index(1)
-            else:
                 columns = Index([name])
+            else:
+                columns = default_index(1)
         else:
             columns = Index([name])
 
         mgr = self._mgr.to_2d_mgr(columns)
         df = self._constructor_expanddim_from_mgr(mgr, axes=mgr.axes)
-        return df.__finalize__(self, method="to_frame")
+        #return df.__finalize__(self, method="to_frame")
 
     def _set_name(
         self, name, inplace: bool = False, deep: bool | None = None