The EGS will not allow reverse to engage when the car is above 7 KM/H if everything is working correctly iirc. It's probably something unrelated. I would try a battery reset.
GT1/ISIS/MoDiC = Factory authorized diagnostic system used by BMW dealerships across the world.
NCS Expert = BMW Factory R&D programming tool available on the internet (not intended for the public and not available to the dealership network)
OEM = Genuine BMW part only available from a franchised BMW dealership.
DME = Engine Management Computer