On a master cylinder changeout, it is often recommended to bench-bleed before installation.
With junkyard parts - you're taking your chances - especially if the brake system was damaged and left open to the atmosphere as a result.
Typically, the booster either works or it doesn't - with about the worst thing being a diaphragm leak that is noticed by the way it affects engine idle speed. Should the master cylinder be hanging up on crud or a nick in the wall - the o-rings won't be lasting long.
Can't think of anything offhand in the hydraulic system that would cause the free play - if there were a restriction in the fluid return flow, the master cylinder should pull fluid out of the reservoir???
It is important to get the booster link adjusted correctly with respect to the master cylinder during a replacement - however, don't know why the original parts had this play.
As for the bleeder screws - yes, they can be a challenge. I douse them with PBblaster for a couple of days before doing any work. The screws always seem to want to round off, adding yet another degree of difficulty to the mix.