From what you describe, I think you have two problems, MC and idle which could be the booster or the vacuum check valve. You can check the check valve easily. disconnect the booster hose whie engine is off. suck air from the enine end. the valve should open. then blow from engine end and the valve should be restricting flow (closed). I am not sure where they placed this valve, in the hose or externally.

The pedal sink is hydraulic issue. It is hard to say what it is. You can check it with engine off. Just pump the pedal and it should be very hard and not sink to floor. If it is, but springing back you have air in the system so a good bleeding of the entire system should fix that. If it just sinks to flor slowly but and not springing back you have a leak either external or internal somewhere.

Note: If the fluid is dark, you should flash it and replace it.