I'm at the next step of a DIY kitchen remodel, and various issues have me stalled out before painting the walls. I have painted interior walls before, so am good with typical prep, spackle, primer, etc. But wallpaper hid a lot of nastiness, and then I pulled off the backsplash. So, here are the problem areas :
1. 2 of the walls have an odd rough texture painted into them- I'm assuming some weird roller texture.
2. The soffits above the cabinet are just rough pine, which was then covered with some sort of filler/ spackled, which was then papered over. It's not even, and has some chips, along with being back to the wood in some areas. I have attacked it with a sander, and do plan on attacking the bigger chipping places again before painting.
3. I pulled off the 1" tile mosaic backsplash, leaving an odd mixed surface. It's a mixture of some old adhesive, which can be a bit rough in places, and drywall with the top layer of paper pulled off. I've attacked it with the sander too, so most of it is somewhat smooth. I've got a drywall patch going on the one big gouge I made.

So, I have read a little about Zinsser's Peel Stop Triple thick, and am wondering if this might be the solution for all of these problems. Would it smooth out the wall enough that I can get a normal roller texture? I was contemplating scraping and sanding the soffit before applying DIF spackle, and sanding again. And with the backsplash, I don't need perfection, as I plan to install some sort of backsplash in the future. I just want it to not look hideous while doing other things, and then be OK to tile over in the future

TIA for any input...