Brake Pedal Goes to Floor When Car is Running

We are pretty sure it just needs a new master cylinder and rear brakes adjusted.
When you hit the pedal it pops then brakes go to floor.
So thinkin the piston in the master cylinder sat in one spot for so many years that surface rust happened in rest of cylinder and that when it was bench bleed it messed with the piston seal causing damage to it and allowing fluid to go by.

As it is right now rear brakes don't engage at all when brakes are hit and the fronts immediately lock up once you hear and feel a pop as you are hitting the brakes.

Just need to order a master cylinder

Myself, I have never experienced a booster being the problem based off doing what you described. Lord knows I haven't seen it all though. Every time I have ran in to that exact combination it has either been air in the lines or a bad component in the brake system. Did you replace the rear rubber brake line too when you did the fronts?