For the random instant stalling with no spuddering, I would suspect a cam sensor going out... If the DME loses cam position signal it don't know the timing for the injectors or ignition coils. If that's the case you may have a fault stored soon.

If not that there is a possibility of the ignition switch going out, slack in the switch could act as if you were turning off the key...

As for the transmission failsafe, there should be faults stored in the EGS that could point out that issue. With both of these problems happening, rather than trying to guess and throwing parts at it I'd bring it in for proper diagnosis. Just make sure where you bring it, if not the dealer, has the GT1 and plenty of experience/knowledge of BMW systems.

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