Finally, the error has been found! It was the thermal fuse S43 that was defective. A friend who is a diagnostician looked at the wiring diagrams and pointed to the S43 – he was absolutely right.
I didn't know there were more fuses there... I had to remove the cover under the steering wheel, and then I found some more large fuses.
Problem with Media 1 and 2 has been resolved by properly logging in

.
Unfortunately, there are still some errors...
01: observe...
03: Monitor and regulate ESP and ABS.
"08er": I can live with that.
34: Occasional, observe.
47er: I can live with that.
61s: THE NEW MAIN PROBLEM.
65: I don't need the tire pressure monitoring system, so it's turned off. Is it possible to disable the warning light for this?
72s: whatever.
Regarding the new main issue:
Idle current... What do the levels indicate?