after struggling long with the installation I now finally solved it.
I will share my findings.
1. Problem: The SD card content does not match with the manual that is delivered with the receiver kit (in my case the version dump1090).
2. Solution: You have to fully update the SD-card by storing a new mirror file. How to do this?
Since I am not a Linux professional it took me long, but once you knkow what you have to do you find it, as it's actually explained well, once you know what you have to search.
Here is the update manual:
A: You need to download the mirror file (thats easy)
B: Install 7zip to unpack the mirror file
C: Install the software to bring the mirror to your SD-card
(make sure to find out the drive letter of the SD card)
D: create and empty file named ssh
Then you have the mirror on the SD-card.
Next: Set up SD card config - now you will find the (before) missing "opensky" folder
A: Enter your longitude, latitude, height, and also username for opensky network. Don't use " for the vales. And remove the # only for the edited lines.
B: in the Settings-File
enter your ID, the one you receive on the opensky-network-page when adding a new receiver (upper corner left). Also take out the # at the begin of the line
After this, starting up the RaspBerry:
C: Put the SD-Card in the raspberry, connect screen and keyboard and start the raspberry.
D: You need to login, with username pi and password openskzdefault (note: standard setting is US-Keyword, so enter openskydefault with the "z"-key in case you have a german keyboard, if not just use the y key.
E: Get your IP, you find how in the regular manual
D: test it in the browser of a different computer with the URL your-IP/dump1090.php and if something appears its a good signal.
That was my process, now it's working!!