You say that the drywall is breaking down. It normally won't break down unless it has gotten damp or wet. I think before you cover anything up you should determine if there is a problem. If there is correct if first. The plaster loosening up is fairly common. It could be for a number of reason, but I think you should still be sure that there isn't moisture problem there too. As far as covering the existing walls without removing the old stuff.....I have personlly covered I would guess 40 or 50 rooms and ceilings over the years without tearing out the old stuff. Is there insulation in the walls and will you ever need it there? Celulose can be blown in from the inside and, of course, that would be done first. If the walls aren't in too bad of shape I go over everything with 3/8" drywall and use lots of screws. Where you are going over plaster and lathe you will sometimes hit studs, but often just the lathe. The screws into the lathe will hold as long as you use lots of screws. Over the drywall you will have to locate and hit the studs with screws. Also on going over the drywall, you will have to end the pieces over a stud just as if you were applying it to bare studded walls. If you end it between studs there will be nothing to hold the edges and the job will be ruined. When I go over existing walls I make sure that any wiring that might be needed is done first. If necessary I make holes to run wire. If there are any real uneven spots on the wall I shim out the low spots with scrap pieces of 1/4" or 1/8" luan or paneling. I don't remove the door and window casings or the baseboards. I run the drywall right up against the casing and fill in any gaps with mud when I am taping. Now a lot of remodelers won't agree with going ovre the existing, but I've never had a problem as long as I've used plenty of screws that are long enough to penetrate the drywall or the plaster. If the walls or ceilings are terribly uneven you might have to use 1/2", but I've always used 3/8".

Everytime you turn on the range hood, it is going to slightly vibrate. And when you run that machine on the higher fan settings, I would imagine it would really jiggle if it's not screwed into something solid. Those bolts might hold it for a while, but I would not trust them for any length of time. I can just imagine the Sheetrock (assuming that is what you have) being worn away little by little. Hopefully, it will just start to sag at first instead of crashing down suddenly one day. Why is adding blocking not feasible at this time in your remodel? Here's a thought if you are just trying to avoid any patchwork to your wall. Mark the wall exactly where the hood will hang. Carefully cut the hole a little smaller then that area. The wall cut out can be smaller then the blocking too. Just partially drill a couple screws in it to grab like handles. Insert the block at an angle, up, then back down. Hold in place and screw it to the studs. You can screw the little piece of sheetrock back over the gap if you want. Everything gets covered by the hood. Hope that is a idea that might work for you.

I costs really very little to put proper framing in a wall and then add your soundproofing

I have found stud finders to be less than reliable There are two types of stud finders. The 'simple' ones are just a magnet that twitches when it gets close to a nail. Those are pretty reliable, but you are finding the nails, not the stud. The other type is electronic and I believe it detects the density of what it's placed on (or something like that). With those types, you usually choose the thickness of your drywall and then you can locate the exact edges of the studs. I've had great success with this type on drywall, but in my experience they don't work very well with plaster. Maybe the plaster/lath is too thick for the detector to differentiate between it and the stud? Or maybe I just didn't have a good enough stud finder.