I'm working on refinishing the walls in the bathroom of my early 1920s construction condo unit that has an alcove tub/shower. The finish will be tile on the three walls surrounding the tub/shower. There is a window on the outside wall, toward the back of the tub/shower. (Orientation: the faucet & showerhead are on the right-hand side of the tub, the long side of the tub is the outside wall, and the back wall of the tub is common to a bedroom.) The plaster-over-gypsum board walls, which originally had a faux-tile covering (vinyl?) on them were apparently not sufficiently waterproof, so there was significant water damage. A prior owner decided the best way to "fix" the problem was to install a vinyl surround that went up to about the top of the window frame. They cut out a section for the window, put up some plastic trim around the window, and did a poor job of sealing the overlapping joints of the surround. Someone discovered that water was getting through those joints, so they added gobs of silicone caulk. Not only did they do a crappy job applying the caulk, the caulk itself eventually became moldy. I pulled out the vinyl surround and much of the decayed/crumbled plaster wall -- the entire outside wall (the one with the window on it), but only the lower third of the back and front walls. The upper part of the front and back walls are sufficiently solid to allow attaching cement board.
So, that's the first question: Is it okay to put cement board on top of the remaining plaster? I can see where the studs are so that it shouldn't be too difficult to put long screws through both layers.
I'm taking advantage of the fully exposed outside wall and installing craft-paper-backed insulation (R-19 -- the "Pink Panther" stuff).
A second question: Is that backed insulation enough of a vapor barrier so that I don't need to put up plastic?
I'm able to get the cement board to mount roughly flush with the rough frame of the window (the part that the vinyl-clad double-hung window attaches to) but unsure about what kind of water-proofing to use and how to apply it. Also, there's a very small amount of water damage to the framing around the window - it's limited to the bottom right-hand corner, for about 2" of the side and bottom of the frame. I figure I can harden that small area with some thinset.
So, the third question is compound: What kind of water-proofing do I need to do around the window and is it safe to assume that thinset will provide sufficient protection from further water damage to those small sections of the window frame?
The attached photo gives an idea of what I'm facing.