Taking things in reverse order:
With the large areas firstly remove any remaining loose plaster. Trying to patch without doing this is a waste of time. Then with the large areas you'll need to replaster. You can either take this as an opportunity to learn or pay someone. I won't tell you how to plaster as it's really a skill you have to be shown or practise yourself, though I do have a couple of bits of advice. Don't try to plaster the whole wall in one go. Take it in stages and make sure you dampen the wall you're plastering onto as it helps the plaster stick.
With the areas missing the top coat of plaster you will need to reskim. This should be done after fixing the base coat. You might find a plasterer willing to skim over your base coat - discuss it before you start. This will give you a good finish but should cost less than hiring a plasterer to do the whole job. Getting a good skim finish takes a lot of practice.
Finally the areas with only minor cracks and bumps should be filled and sanded before proceeding.
If you manage to get a good surface then painting is the best option. If not then paper the wall with two layers of lining paper. The first runs horizontal and the second vertical. This will smooth out most of the remaining unevenness in the wall. Before papering wash the walls with a weak glue solution this will stop all the glue from the paper being absorbed into the plaster and the paper lifting off the wall.
I should have added that you need to leave the plaster to fully dry out before painting or papering. That might have been one of the reasons why the previous repair has failed.
UPDATE
The quote you have doesn't seem unreasonable but without knowing the exact area you need replastering or your location it's difficult to say for certain. However, we shouldn't be getting into commenting on exact quotes as they are always going to be too localised (in time and space). Get another quote to compare it against - that's always going to be the best option. Also as I said above see if you can get the plasterer just to do the final skim - it should come out cheaper.
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
Unless you have a remarkably uneventful time removing wallpaper you are often left with a surface less than ideally flat and having a mixture of different sorts of detailed surface types (stubborn last bit of paper, bare plaster, glue, old paint etc.)
You may want to consider a skim coat of drywall compound over the whole wall to remove minor irregularities and to provide a consistent base for the paint. In most cases it will be obvious if this is more or less sensible than a primer/sealer coat of paint if you have the idea of both in mind and look at where your walls end up when you get the paper off.