How can I remove the tile without damaging the plaster? Also, can I just tile over the plaster for the shower area, or should I do something else to waterproof it?

Thanks in advance!

There is no real way to remove them without causing at least some damage.
If they are held on with mastic, a heat gun can soften it, but you are unlikely to get the rest of the mastic off the wall without some damage to the plaster.

"Also, can I just tile over the plaster for the shower area, or should I do something else to waterproof it?"

Tile walls still allow some moisture to penetrate, if only at the grout joints.
You might have a wall that used Keene's cement instead of plaster, and it should be resistant enough to moisture to tolerate tight grout joints.
Older houses usually have a 'mud bed' of mortar on the wet walls around a tub. It is a few inches thick and very water resistant. More mnodern work uses cement boards that are about 1/2 inch thick, and still can allow water movement so another membrane layer is added between the cement board and the studs for protection. Kerdi is a plastic type membrane, or even 15 pound tar paper.

Green board is not going to last very long behind tile in a wet location like a shower.

In about 10 years (possibly less) you will be removing the tile and green board to replace it again.

While tile can be water tight, the grout joints are not. Water will wick through and destroy the green board.

I just finished tearing out a tub surround in a rental house that was only about 8 years old.
It is used twice a day for showering, and was completely rotted. Tiles started falling into the wall.

Cement backer board (and even that still requires another membrane layer, if only tar paper, is the correct backer for wet locations.

There are membranes like Kerdi available that are water tight, but drywall is still pretty flexible stuff for tile to be applied on if it can be bumped very much (like a shower wall).