The reason for waiting is to ensure that the plaster dries completely. If you paint over damp plaster the moisture has to still come out - through the paint causing it to bubble and come away. You will end up having to repaint at the very least.
If you have only patched the wall then you should be able to prime and paint it sooner as there is less area to dry.
However, I would leave it as long as possible before painting, just to be sure.
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.
Best Answer
The blisters in the photo are due to moisture (water vapor) being forced out of the from the opposite side or from the ground. Moisture permeates through the plaster in the path of least resistance, such as a fissure or hairline cracks. If the surface has been painted the water will actually blister the paint as it continues through the wall. The powdery residue you notice is a combination of minerals left behind when the moisture evaporated and whatever effluence it picked up traveling through the plaster. To solve the problem first eliminate the cause of the moisture. This could be any thing from a wayward sprinkler that splashes water against the walls surface to gutters saturating the ground that is against the wall. If the wall is in contact with the soil, excavate to the footing clean the surface and when dry apply a concrete sealer like Dryloc. To repair the blisters wire brush the loose plaster scrape any flaking paint, apply a concrete adhesive to the surface (not critical to the repair, but it helps), and apply a plaster patch as needed. It will blister in another location if the water source isn't corrected.