Yes, expect to have a huge mess. I had a bathroom with that problem. Since the surface was vinyl, I had to remove it. The mess was terrible. I got the vinyl and the paper backing along with a lot of the drywall paper off the walls. I coated the bare gypsum with Gardz. When it dried, I kept filling the deepest dents with thin layers of joint compound, then eventually did a skim coat of the walls. More Gardz, good primer then two coats of paint. It looked good and held up well. But it was a lot of work. Having removed layer after layer of painted wallpaper, it's not something I recommend. A lot depends on how picky you are. Painted wallpaper never looks great, but you may decide that it's "good enough" when compared to the work to remove it and patch the walls. If you go that route, you have to remove any lose paper, sand lumpy seams, etc. then seal it with Gardz, then prime and paint. It may still bubble or loosen, but that's your best shot if you want to paint over it.

I've used goo-b-gone or goo-off from HD/Lowes to remove caulk from drywall. Just spray it on, let it soak-in for a minute and scrape-off with a putty knife.

They make a little tool that helps in removing caulk.It has a little hook on the end to help pull it out. Any paint store should have it. I'll guess that your builder used the wrong kind of caulk. It needs to be specifically made for use in the bathroom in wet areas AND it needs to sit for 24 to 48 hours before you get it wet. Heating it can help. Use heat gun or a blow dryer. For indoors I prefer the blow dryer. When you go to redo it. Cut the tip of your caulk at a angle and make it smallish this gives you better control when the caulk comes out. Remember if you click on the gun handle it should stop the flow of the caulk. Use a wet finger to gently push on the caulk and in a single continuous stroke move your finger across the caulk. Any holes just dab a bit of caulk on your finger and press it in and then run your finger across the caulk line again. It takes some practice. Trick is not to be afraid of making a mistake with it. Worse comes to worse you wipe it all off with a wet disposable rag and do it again. Some folks I know claim using a piece of plastic cut from a detergent bottle to spread a smooth caulk line is the way to go. I've never done it because I think my finger works just as well but it's something for you to try.

I'm not a professional and it depends on the size of the area to be repaired, but it's pretty easy to cut out damaged dry wall and then mud the patch seams. You want to do whatever will maximize the clean, level surface. And, yes, you will need to feather and sand your mud until it is dead level. I wouldn't paint the mudded, repaired drywall before tiling, at least, I never have. And I've never primed drywall before mudding it. If you've only read or watched videos, be sure you practice. If your repair area is large, even if just 'paper', maybe hire somebody?