This seems like kind of a basic question, but I could really use some suggestions. Long ago I painted these walls with no thought to try to smooth them. I've read about putting a skim coat on and then sanding, but I'm not sure what this surface it. The medicine chest opening is awaiting a suitable vintage replacement so it gives a good cutaway view. I don't think that's drywall. My thought is that there was wallpaper which left the walls so rough. Also, the area where the tile meets the wall is not good. Should I just sand the present surface?

Also, I remember the ceiling was peeling and I scraped as best I could and then painted. Again, skim coat or I'm thinking just paint over (it doesn't look too bad--unless you look up!).

Primer first and then satin for ceiling and walls?