EGR, exhaust gas return. It's a valve used to introduce exhaust gasses back into the intake stream to lower combustion temps and reduce NoX emissions (not always equipped).
Smoke test IS the most effective way to check a vac system, do behind the throttle plate and then in front to check both sides for leaks.
The brake sensor won't keep the car from starting/running but if the brake service light is on cruise control and abs won't function.
If no leaks turn up your last best option will be to take to a shop that does or at least has experience w/beemers and have the sensor data reviewed while the problem is occurring. Could be an ect (engine coolant temp) sensor or equivelant giving a faulty read and causing a limp mode in the ecu (engine control unit)