Depends on many things but less is better. If the model will be used with all the parts it does not matter if they are separate. Less materials is better performance wise. So ideally one texture / one material for whole model.
You can make 4k textures but no game these days is using 4k textures, it's too big. So it should look good with 2k max. If you can't stuff it all in to 2k then you should probably use more textures.