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.
Before you attempt to repair it, make sure that the cause of the ice dam has been fixed. You may need to insulate the ceiling, and/or add a styrofoam vent baffle to the inside of the roof to prevent that area from getting too warm. Ice and water shield installed on the roof probably would have also prevented this from happening.
The repair will depend on how long the wall was wet and the extent of the damage. From what I am seeing, you should be able to fix this damage without needing to pull the whole wall apart.
Let the wall completely dry out and then check for signs of mold growth. A dehumidifier is not going to dry out the wall for you. You will also need fans aimed at the wall to circulate the air. Industrial blowers will do the best job, but a household box fan on high will also do.
Mold may be on the surface of the plaster, and it could also be under your trim. Use white vinegar to clean off the areas affected by mold and then use a mold killing primer such as Killz on all of the damaged areas.
Once the wall has been primed, then you can repair the plaster. You will need to get a bag of plaster of paris and a 5 gallon bucket of drywall joint compound. Mix the plaster with water per the instructions and mix in joint compound in a 50/50 ratio. Trowel on the mixture and blend the repair into the existing wall. The advantage of mixing the two is that you can use thicker coats of plaster without having it crack. It will also dry much faster and shrink less. The joint compound will make the repaired area harder and will bond better with the wall. Over time plaster dries out and becomes brittle. The gypsum in the joint compound will help prevent the plaster from deteriorating. In the old days, they would mix in chopped up animal hair (usually horse hair) to strengthen it instead.
You may need to apply more than one coat. You should also sand lightly between coats and feather the repair into the wall as best as you can. Any imperfections will be easily seen once the wall has been painted.
Once you are satisfied with the repair, then you can prime the wall. You can use any kind of primer that is compatible with the color coat. I prefer using primer that is rated for interior and exterior use since it is less likely to peel when you put the final coat on.
Repaint the wall and trim. If you can, repaint the entire wall at once so there isn't any differences in the sheen. It may look different if you only paint the damaged part.
Once the wall is painted, you shouldn't be able to tell that there was ever any damage there.
Best Answer
At this point, I don't think an old-work box can be used. As bib mentions, you need a sturdy surface to attach these. You also have a plaster repair in your future, so if you're going to patch that, you may as well go with a new-work box. You have two styles to chose from, one with a tab that attaches to the face of the stud and another that nails into the stud:
I'd recommend the version that nails into the side of the stud, but I'd also recommend swapping out the nails for screws. The process of nailing this box in will disturb a lot more of the plaster.
Go ahead and open the wall up enough to install the new-work box, get the cables inside, screw it to the stud, and secure the wiring with staples to the center of the stud. Then patch your plaster by installing some backing material, applying the plaster with a wide knife, and smoothing the joints so they can't be seen with a light shining at a sharp angle.