UPDATE
Sooooo... 1 1/2 years after this issue started it seems the main problems have been fixed, but not all of them. As suspected near the end of the thread, the passenger side door lock actuator went bad. It wasn't locking when pressing the remote button, so everything would momentarily lock, the brain would find something wrong with the passenger door, and everything would unlock again. So now the security system can be armed and both doors can be locked.
So that battle was won, but not the war.
The gas lid lock still stays locked, the trunk won't open with the remote, and the alarm won't chirp when armed/disarmed. Also, a few months later the trunk level locks stopped working (in locked position, of course) but that seems to be unrelated. Are these separate problems? Is it just a (huge) coincidence that these things went wrong at the exact same time as the door lock actuator or are they related? Why did the actuator go bad after a strong rain? Was that a coincidence too?
I have more questions now than before
But I'm happy that the electrical system is almost back to normal
