I'm having the exact same issue with mine - originally the range extender would work intermittently, sometimes I would get 50miles and then have to leave it for 15 minutes or so, and then maybe get another 5-10 miles out of it. After a while it would be more like 5-10miles and then for a while it wouldn't work at all.
Firstly I swapped out the fuel pump relay, and all of a sudden it was working again, but then after 20 miles of use I was getting the same drivetrain errors (only electric range possible, etc.). So then I tried replacing the 12v battery, as the car had fully died one night in a car park after having interior LEDs on while vehicle was in park - so seemed logical that a dying battery was the cause of the range extender failure.
After replacing 12v, again it seemed to work perfectly, got maybe 20 miles out of it however and same drivetrain errors again. However it does seem to work a lot more regularly than before, whereas before it would sometimes not work at all/max for 1-2 miles, whereas no most time I will get 20 or so miles out of it.
Also got the same fault codes as you as well as 117000:
117000: Fuel tank pressure/temperature sensor circuit: Malfunction or open circuit
105002: Crankshaft sensor, signal sync error
114001: Engine oil pressure switch: switch is closed
D04C1E: sub-bus failed/tank pressure sensor does not respond.
Also the interior lights seem to be blinking as though the 12v is dying, however as I have just replaced it I wonder if this is just an unrelated fault such as the LEDs themselves going, however I'd be curious to know if anyone has experienced similar electrical faults alongside the range extender issues.
Have you or anyone with similar issues had any look getting this fixed. I tried taking to a BMW garage initially, but there approach was to run a "fuel sample test" for £300 and add some additive to clear any carbon deposits, and if that failed to fix the issue (no surprise it didn't fix anything), was a fully REX replacement which would cost £3-£5k