Can I save these bathroom walls?
Why would you even try to save this mess?
New drywall (which could be proper water-resistant drywall) would be much faster than extensive repairs to a suspect substrate, and result in a better substrate for whatever you do next than patching that mess.
If you intend to tile, replace with cementboard/backerboard (at least in the tub/wet areas.) Far superior, at slightly increased cost.