Welcome, Chuck.
1. Site specific question and I can't see it from here. Those colors suggest it might be a mudded wall with rounded "mudcap" edges. You may or may not be able to remove the tile and mud, but it's frequently easier to simply cut the sheetrock (if it's sheetrock) around the tile and reomove the whole thing.
2. You can do any of those things. It's not considered a wet area. If you know it'll
be a wet area in your installation, use the CBU, at least.
3. You must leave a space of 1/8" or so and fill it with flexible sealant (caulk).
4. Grout type is dependent upon grout joint width. Industry standard says for joints 1/8th" or less, use unsanded. For joints 1/8th" or greater, use sanded. I prefer to use sanded until the joints are just too small to force sanded into'em.
My opinion; worth price charged.