OK, after 4 days (and waking up in the middle of the night with an answer which was correct) I finally got root. Getting root is easy if you know where to look. I did a huge facepalm when I got it.
This is my hint for all who are starting with this machine:
In order to find the right entrance you need to knock all the possible doors, not only the obvious ones. Then use a famous exploit and you’ll be in. Then just follow the footprints all around 