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.
The fact that sections are peeling off indicates that there is a structural problem with the overall "sandwich."
In any repair, unless you can overcome the structural deficiencies with an overriding mechanism, you have to strip back the unsound sections until you get to good structure. With you description , it is hard to see where that is.
You could knock loose all the compromised sections and then try to patch the open areas, but it sounds like the overall lathe-plaster-chicken wire-plaster amalgam may be questionable. You may do this and shortly thereafter find a new section that is failing.
I think that a drywall overlay may be the simplist, fastest and cheapest solution, by far. Whether you strip down to the chicken wire or to the lathe depends on how much of the ceiling is loose/compromised. If height is not a problem, dislodge whatever is loose, use shim to insure level and then screw up thin drywall over the whole ceiling. DO NOT USE NAILS! If you hit studs, great, but the lathe should be adequate to hold a thin wallboard lamination.
Best Answer
The plaster is sagging probably due to issues with some of the lathe boards above it. Those need to be repaired.
If you have access above this you could just knock these totally out and reframe with 2x4s. This would probably be the quickest way.
As far as mess... You are thinking about this wrong. Demoing might be a mess. Sanding the mud for the new drywall will be 10 times worse for your house.
My advice is knock out the ceiling. (this will take minutes) Then reframe and then add drywall. This space will have to be totally emptied out. If you are quick you can get drywall up with first coat of mud in day 1. Day 2 you can add second - final set of mud (if you are really good). This will take at least two days to dry. Day 4 you are sanding. That is best case scenario. Room will have to be emptied and doorways will have to be tarped off from rest of the house.