rotted plaster wall underneath kitchen faucet leak
Hello, would love an opinion on this.... We have a 1949 bungalow in SE Michigan and recently discovered the back wall under the kitchen sink was crumbling, and some evidence of minor water leaking in the basement just below it. I had my dad look at it, and it seems like the sprayer pull-out faucet that came with the house when we bought it in 2004 has been leaking and dripping onto the cold connection pipe that runs into the wall, traveling along that pipe and into the hole where it inserts in the wall, probably for a long time. Right now it's hard to tell if there is any other source, but we got an opinion from a former window installer that it doesn't look like it's coming from the kitchen window above the sink.
Had a plumber out to change the faucet, he didn't see any obvious problems with the pipes and fittings (at some point they were changed out to copper pipes), but he didn't go digging into the wall. I did some more poking around that crumbly area after he left, and it's really breaking away, I'm down to wet insulation and some black wood next to the copper pipe, I didn't realize it was wet back there, I thought the damage was just to the surface plaster. I can poke a pen several inches into the wall past the pipe, and it seems like there's some wet, sandy stuff in there, too (mortar?). The wall about an inch or two above where those pipes go into it seems pretty solid.
Just trying to figure out if this is just residual dampness from the bad faucet and a fix we can do ourselves. If we open it up a bit more, get out what wet stuff we can reach and let it dry out, maybe hit it with some bleach, I assume we'd then need to re-insulate and patch up the hole so the pipes don't freeze? Do I need to worry about any rotted wood if it's not supporting something? Is there anything else I should be looking for as a potential alternate leak source other than the faucet?
We're way underwater with a yucky old kitchen, so we don't need to get fancy, but I want to fix it well enough so that we don't have more expensive issues later should we decide to stay for the long haul.
Thanks in advance for any suggestions.