if your brake booster is bad and is replaced, does the master cylinder need to be replaced also?

These are all very astute questions. I really feel, after reading them, that you have multiple problems in hindsight. a hard pedal can be caused by pads effectiveness, Their lining condition, material makeup. and condition of rotor surface A hard pedal can be caused by caliper issues. It can also be caused by a failed brake booster, leaking booster, or insufficient vacuum or vacuum volume, a failed vacuum check valve, The fluid can leak from the master into the booster. Why did you have a loss of pedal after the booster was replaced? instead of the hard pedal you had before? perhaps boost was restored, and your symptom's feel changed. perhaps they opened the hydraulic system allowing air to enter? You would have to test each time you changed something or received the car from them. Worn linings, if that's what you found, needed replacing. they can cause low pedal. Bleeding the brakes after is normal maintenance to have fresh fluid and getting the old "wet" fluid out. That should restore your pedal if air is trapped. If your system requires a bleed tool for ABS, you may want them to continue till they have a pedal, or replace the master and bleed it to restore a good pedal. When you have that....You can trust your brakes. You always have the option of a German car shop or a brake shop to verify the findings told to you. The circumstances seem strange the way you describe them... but you have to get your facts at that moment, to draw any conclusion. We cannot do that from here.

The one other anomaly, is allowing the pedal to bottom out, during parts replacement. That can hurt seals. pedal bleeding would have just been needed if they were replacing the part you say is now failed but was not replaced. so, did they maintenance bleed it? we cannot see that either.

I'm having a problem with my 745 BMW someone please help it's telling me that my brake liner is broken so I checked it out is this the reason why my vehicle doesn't start