Replace that section of wall with drywall.

Move! Run now! :-)

seriously though, how extensive of a renovation were you planning? It's galvanized pipe which has probably built up with a bunch of sediment over time. Ideally you would want to replace it with copper/Pex, but that kind of opens up a can of worms as to how far back you would want to go. It's nice to have new pipe running into new fixtures, but you won't get great new water pressure until you replace most of the pipes.

As for the wall, that's crumbly plaster and it is pretty loose - hard to tell how big the area is, but you could get out what falls out easily, and put a patch in.

We reno-ed our bath that was plaster, saved the original floor tile, etc... We did it by working on one thing at a time (electric, patch walls, plumbing, patch walls) Because of our family/home layout, we needed to keep as much of it operational as long as we could - in hindsight if we could have just gutted the whole room it would have been a bazillion times easier.

Yeah, right now we're not looking to take on a major renovation. Truth is, it wasn't that bad until husband had a friend come by to "fix" it. It was acceptable and everything was working great to me before the friend - but husband wanted perfect (in an 88 year old house!)...and now here we are. Patching/new drywall is where I'm at with it for right now. The room paint is a darker shade and the imperfect wall really didn't look too bad at all pre-friend so hopefully that'll be the case post-friend.

If all you are looking for is a cosmetic fix, you could get a tub of patching plaster and apply it and smooth with a putty knife. Then prime and paint.

Patching plaster

Replace the pipe with copper or PEX and then fill the hole with wire lath and Structolite plaster.