Edit:
The issues got way better since I'm using a VGA-Cable.
1) The overscan is gone since now I use the PC-mode of the screen which disabled overscan
2) The image is a lot more stable. It looks crystal clear in the beginning, however after 5 mins (and not 15sec as before) I start getting artefacts, which keep ketting worse and worse. Unplugging the cable and inserting it right after doesn't help. I need to wait at least some minutes until I can repeat the process.
Any Ideas?