Well, I will send the printer back tomorrow and get a new one. Just looking for the "right" one.
Regarding the nozzle: There were different wires included, but I had no chance to free the nozzle. So after replacing it, printing worked, but I run into the issues that you described. Biggest blocker for me was that due to a manufacturing issu, I could not remove the cover from the hotend (where the fans are installed) so it was very tricky to exchange the nozzle at all.
In the end, I had a printing nozzle, but also the all the plastic around it which finally even caused that something "burned" into the print bed.
And btw, thanks for your explanation - the forum where I tried my luck to get some infos how to solve it were very rookie unfriendly - in the end, the moderator replied with a single "read!" and closed the thread.