Do gas giants have southern and northern hemispheres?
Yes. All planets have northern and southern hemispheres defined in terms of their rotation.
We define the north pole of a planet as the pole of the planet that's north of the invariable plane around which planetary orbits are clustered (https://en.wikipedia.org/wiki/Invariable_plane). North of this plane is in turn defined as the same side as our own North Pole. Northern and southern hemispheres are then defined accordingly.