yes you can float a concrete pool- there are some barges made from concrete, so it will float in the right shape, and a pool has plenty of empty volume; less likely than fiberglass, but can happen especially if water table is high/ground is wet.
I would consider a half drain and fill as a potential time and money saver- if you're confident of the 120 number, 1/2 would be 60 and not a bad place to be for CYA, and then only have to replace 1/2 chemicals.
vitamin C does clean up some metal stains
As you add water, you can add bleach pretty much as soon as water covers bottom- maybe 6 inches, just keep it stirred manually.
I would add calcium once you get water circulating
don't think I'd mess with alk until completely full, and you see what the pH is doing; alk is pH stabilizer- if pH is stable, don't need alk.
also, Borates can work well as pH stabilizer, and also helps water be crystal clear!