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.
I would be more concerned that your wire looks to be at the very bottom of the concrete, making it useless. Concrete is very strong under compression but very weak under flex. The steel is there to take the flex and should be about center of the concrete. Definitely use a concrete bonding agent and Ditra. The Ditra will provide enough of a barrier that the cracks should not come through. Personally I would not put a huge pile of money into tile considering it might end up cracking
Best Answer
(I was lucky with my last cooktop - it was slightly smaller and my plumber was able to cut the counter a little bit to make it fit.)
With a stainless steel cooktop, I would look for stainless steel - or at least "shiny metal" to match. Something like this one on Amazon:
Definitely measure first! If a filler piece is too long, you can cut it down, but if it is too short then it won't work very well.