How to repair nail and screw holes if I don’t know if wall is drywall or blueboard

I don't think you'll be happy with spackle for anything bigger across than a nail hole. It's not very strong, and also not very sticky. So what tends to happen in your situation is that the spackle will fall through the hole into the wall; if not when you're applying it then it will be likely to do it when you try to sand it smooth before you paint.

I think the solution that's going to get you the best results for holes that size would be to cut a 2" square of fiberglass drywall joint tape and stick it over the hole, and then use joint compound to fill the hole and cover the tape, feathering it out to a 6-8" diameter circle. You can do this reasonably well with a cheap 4" putty knife. Then sand it smooth, being careful not to sand all the way through to the tape.

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.