If wallpaper was painted over you could tell pretty easily by pulling on some of the peeling paint and breaking the paint chips. Wear a respirator mask while doing this, however, as often times flaking paint is a potential indicator of lead based paint. If the chips contain paper, then you're right, it's wallpaper with paint over it. If it's just paint, then be more careful - get the chips tested for lead.
Given the wide spread flaking, it is likely that the wall simply wasn't properly primed. An improperly treated wall when painted over will eventually lose adhesion with the paint and it'll flake away like you're seeing. If they applied paint directly to wall paper w/o priming, I think the same is true.
That 2nd picture DOES remind me of wallpaper... I've scrubbed far too much backing off the walls and that looks similar.
The grey subsurface is, I think, a kind of stucco mix that was often used to even up walls where lathe and plaster was replaced with the older style 2x4 drywall panels. It's nasty, gritty, dusty, unpleasant stuff, tougher than joint compound/plaster to work with because of it's tendency to crack and break rather catastrophically. When I run into that stuff in my rentals my approach is, "IF I have to touch it at all, it's ALL coming down." Plus with wallpaper I swear gutting is easier than stripping.
Now around the vent pipe, that looks like moisture damage. The bubbling around the pipe suggest water leakage. Is that a "finished" ceiling - ie - thats the roof on the other side of that wall w/ the pipe? If so, make sure it's properly sealed and replace at least that area of ceiling.
Picture #5 seems to confirm this - someone touched it, and patched it badly.
Did the countertop installers also install the backsplash? If so call them back and have them correct the issue. That seam should be sealed for appearance and to prevent any water from getting in there.
If the backsplash was already there it could be that they did a poor job leveling that section of countertop or the backsplash wasn't level.
Either way, call them in to look at it and correct it. Might just need to run a bead of caulk and they'll have the right color to work with the stone you selected.
Best Answer
Scribe it. Use a compass (or a stick with a pencil attached to it) set to the widest gap - run the compass or stick-with-pencil along the wall, marking the countertop a set distance out from the wall. Cut along the line - if done carefully, the wavy edge of the countertop should now fit the wavy wall precisely.