Jumpstarting a BMW in general is a pretty bad idea.

And yes, 100% you can royally screw up synchronization of your various modules with a bad battery and low voltage.

I had this same problem with an old e39 I was trying to bring back to life. Car started and I drove it home. Battery was bad, didn't want to replace it, and went to start it - CLICK. Died never would start again because the EWS lost sync. And it fried my Transmission control unit.

Spent WEEKS hunting through INPA to figure out how to resynch the codes and get it to start, and was fortunate an e39 TCU isn't coded to the car.

A painful lesson. Get a good battery before trying to diagnose other (esp electrical) problems.

Also +1 on a real scanner OR a machine with INPA. I use a Launch X431 mini