first, you need to establish why the battery was drained... twice... was it under normal operation, like you drive the car everyday, and the battery just died... or, you left the car parked at airport lot for a month and the battery died after that...

regardless, it has been well documented that the E53 is very sensitive to the internal state of the battery and the charging system - if the battery is less than "perfect" (perfect is an overstatement), a lot of electrical systems inside the car will behave erratically - you may have random headlights turn on, the windows roll down/up on their own, radio turn on/off, tranny go into failsafe mode...

If the conditions that drained the battery twice will not repeat themselves under normal circumstances, first thing I'd do - replace the battery that had been drained twice, and thus is compromised...

if the battery was discharged under normal drivnig conditions, i'd check the charging voltage of the system, and the alternator in general...

in these cars, before repairing things downstream, you need to get the source squared away - that is the battery and the alternator...

It was alternator actually. I replaced it now. Before changing the alternator my garage guy lend a spare battery which was fully charged. It did not help..and he concluded it is alternator.

Yes, you are right, between these two jump starts, computer has show lot if errors you described above. Now I am over this problem with battery. Batter charge is showing at good 13 amph.