Yes, there is no problem in using latex in a bathroom. Oil based paint would hold up longer if the walls are being scrubbed down, but it's more difficult to work with, costs more and smells worse.
The only thing you can do is wait, until it evaporates. Stir it every now and then.
yes
No But you can put oil based over water based paints.
If you really want to ... yes. It might cause some issues later but should work for the most part as long as you apply a thin layer of paint.