To put up shelves on a plasterboard wall you will need to find 2 studs to which the plasterboard will be attached to.
You can use any adhesive and the method to apply it is "dot and dap" which is evenly spaced dots around the plasterboard to make sure it sticks well.
You should nail or screw every 300mm around the ends of the sheet and any openings.
Yes, plasterboard is 100% waterproof and compliantly non-combustible, so it is ideal for showers and bathrooms where there will be a lot of moisture in the air.
The ideal adhesive is Unibond No More Nails because it's strong and ideal for heavy-duty adhesion and it eliminates the need for screws or nails.
Definitely make sure the plasterboard is sealed before painting. Give it a light sand down to make sure that the surface is smooth but don’t use silk or vinyl on bare plasterboard.
It is fine to tile on it as it is, you could do a coat of primer but it’s not necessary.
Do you need to seal plasterboard with PVA?

No, never seal plasterboard with PVA. Before painting the new plaster, you need a sealer to prime the surface.

Don’t get the plasterboard soaking wet, just get it damp by running a wet paintbrush over the plasterboard. If it is absorbed instantly then go over it again and then leave it for at least 10 minutes.
No, you do not have to. You can decorate and paint over the plasterboard.