Brake flush and bleed

I would do the flush on the old parts to avoid running dirty fluid through the new parts so yes it is more than OK. Make sure you flush both ends and do not let any air into the system. If this car is used in a rust belt state you would also want to check all of the hard lines for rust and possibly replace the rubber flex lines due to age.

I would not do it that way because when you push the pistons back, you are going to push all that fluid back into the master again. If you do it the right way and open the bleeders when you push the pistons back, you can avoid that but nobody ever does that.