Only following primer.
There are several types of paint you can use depending on the result you would like to achieve and the area you are covering. Matt, eggshell, satin and gloss all can be used on drywall with different finishes.
noo!
Yes, you can.
It's generally much better to use water base primer on drywall.
Drywall primer should be used.
If you expect your shower to last, then remove that drywall and re-finish it with concrete/fibre board. It's so much better than drywall you wouldn't believe it. Nobody professional does drywall around a shower anymore.
If by top layer you mean the paper, then re-install drywall on that wall.
The drywall wasn't primed properly.
After mudding and sanding, primer is next, then paint.
you dont..... you can by a paint product such as " Zinser " or " Kilz" to spray to block it from coming through your drywall. it comes in a spraybomb or gallon.
If you used the right paint, Bathroom paint, 2 top coats, over primmer,over greenboard primmer, over greenboard or paperless drywall, then no.