I am going to be tiling a wainscot. I will be using the height that works for me in relation to my other elements. My vanity will be a 36" counter height with 10" stone backsplash all placed in front of the wainscoting. I adjusted the height of my wainscot to accommodate my design plans. Mine will be at 50". I've seen shorter and taller. I don't think there is a set height. My ceiling is only 7' high. Here is an image that gives proportions. My room is 9.5' long, and includes the depth of the built-in floor to ceiling cupboard on the right. As I said the ceiling is 7' high. The floor is just there to help me visualize pattern and color. As you can see the mirror that I am considering barely fits above the wainscot and the ceiling :/ The square on the left is a cut section of my 60"x32"x14" high tub. Having everything all drawn up to scale is wonderful to plan properly & to avoid surprises.

Waterproofing the most overused word on this site. Tiling walls is a regional thing. In the NE it is just about mandatory but out W you will never see it. A good fan and proper placement is what is needed. People instal fans but don't take into account where they draw air from. If you have a fan near your shower and have an open window in the shower it will only pull from the window not exhausting the room. It might sound odd but it should in that situation be placed on the opposite side of the room. If you place it near the shower and have a door on the opposite side make sure the door is cut a bit high so it can pull air. Fans don't need to be on for an hour or 24hrs thats ridiculous and you need a better fan and better placement if that is needed. Probably one of the best defenses for moisture is a simple lightbulb. Exhaust fan with humidity sensor built in will go on and off when needed. They sell miniature dehumidifiers if you are that sensitive and need the air that dry. They come in both mechanical and chemical reactive non electric versions.

I will pass on what I learned from a very good acoustical consultant I used for several high-end housing projects. Hard vs soft finishes only change the reverberation of sound within the room. To reduce sound transmission through the wall you need wall materials that provide mass, absorption or resiliency. All 3 is best. The mass of ceramic tile and the absorption of fiberglass insulation are both minimal unless the tile and the wall were tripled in thickness. The usefulness of Insulation in a wall with a door is less than minimal even if its a solid-core door. Bathroom doors invariably require an undercut in order for the exhaust fan to operate so they cannot have the necessary acoustic device at the saddle. If the wall is already built, add a layer of 5/8" drywall to the side with the fewest penetrations. Carefully seal all penetrations, Sound abatement beyond that involves adding a resilient layer behind the added drywall or using a resilient drywall product or adhesive.

I had a product like that called Baker Board in my last bathroom. It was sold for use in the bathroom to mimic wall tile. It is basically a kind of panelling that looks like bathroom tile. Mine was from the 1990s and looked nicer than yours, but was basically the same thing inside. We had ours installed over drywall. I suppose it is possible that yours is there in place of drywall. Mine was stuck to the wall board with construction adhesive. It is always possible that someone glued yours over really bad tile, to keep from having to tear it out, too. I think it is hard to say until you get behind it.