Last year I bought a similar old home circa 1895 that had a mismatch of old and new plumbing, galvanized, copper and PVC. I had leaks, slow flow & stuck valves. After 3 days of fixing one place only to find the problem moved to a new location I gave up and replaced the whole house with PEX all the way back to the incoming pipe. I built my own distribution manifold hot and cold and ran ½ from there to every location in the house and did it in 2 days. Flow has never been better and water quality is much improved.
My previous home was quite similar and I wish now I would have done it all in PEX. Looking back at all the time I spent here and there working on it over the years.
PEX is very DIY friendly once you have the few tools required.
As to cleaning out the rust I never found a good way and I had pipes that had rusted shut to just a pin hole. Every time you disturb them some of it comes loose and moves making a new clog. It’s like a dog chasing its tail.