Fix binary operation column ordering and missing column issues

[galipremsagar]

Description

This PR fixes various cases in binary operations where columns are of certain dtypes and the binary operations on those dataframes and series don't yield correct results, correct resulting column types, or have missing columns altogether.
This PR also introduces ensuring column ordering to match pandas binary ops column ordering when pandas compatibility mode is enabled.

Checklist

• I am familiar with the Contributing Guidelines.
• New or existing tests cover these changes.
• The documentation is up to date with these changes.

[galipremsagar]

Note that there is some intersection with changes in #13772

[wence-]

I think this looks fine with one comment that we can potentially avoid one "expensive" check?

[wence-]

Can we do the cheap thing first So that we don't convert to pandas and check equality if we don't need to?

[galipremsagar]

We could change this to something like this:

if cudf.get_option("mode.pandas_compatible"):
    equal_columns = other.index.to_pandas().equals(self._data.to_pandas_index())
else:
    can_use_self_column_name = (list(other._index._data.names) == self._data._level_names)
    if not can_use_self_column_name:
        can_use_self_column_name = other.index.to_pandas().equals(self._data.to_pandas_index())

[galipremsagar]

Switched to a cheaper condition first.

[vyasr]

LGTM

[galipremsagar]

/merge