This looks like older plaster and thus may have some inherent texture to it. But the linked photos also make it look like the paint is very high sheen, like semi-gloss, even on the ceiling. A high sheen paint is easy to clean but will show every imperfection. Something more flat will hide those imperfections. I like to use matte everywhere except kitchen and bathrooms, and only use semi-gloss for trim.

“Alaska’s arduous Iditarod” is some great alliteration

It’s the new Linux kernel

You can try replacing the flexible supply line first—I’ve had those become obstructed with god knows what I’m the past, making the toilet really slow to fill. But as others have said, don’t try to just replace the valve, you’ll need to replace some lengths of pipe as well. Looks like it may be galvanized, in which case you can screw some new pieces together or replace with copper or sharkbite. As for the floor, don’t worry too much about how to clean it, if it were me I’d just live with it until it’s time to replace. This bathroom likely needs to be redone!

Sounds like an expensive project! I’ve attempted several floor leveling projects in our 110 year old clapboard house with its floors being angled this way and that due to joist sagging etc., and have had the most success combining a couple of approaches. First I would definitely remove the new floor (d’oh!). Then cut out the subfloor in the worst affected areas, i.e. the most saggy. Sister in new joists with lots of glue and screws but make the new joists as level as possible, that way you can avoid fiddling too much with shims, etc., although getting the new subfloor even with the old does take some finagling. There will almost certainly be areas where sistering is not possible due to other infrastructure in the way, so it’s up to you how involved you want to get with that (moving electric, plumbing, ducts, etc.). Sometimes you can sandwich plywood on either side of an existing joist to strengthen it and that takes up less space and works pretty well too. The main idea here is to add strength to the joists and also level them a little bit.

Once that’s done, and the new subfloor has been added, you can use leveling compound to level the floor out the rest of the way, and you won’t need to worry as much about the added weight from the leveling compound. I’ve only done this in areas where the floor was going to be tile or carpet although I believe this will also work with engineered wood flooring (but not regular hardwood).

Good luck! This is a big disruptive job that will take a while, just be careful and don’t fall through the floor.