I need to write my answer in English as my German is almost non-existent.
Your debug log shows lighttpd was not installed and you are running Apache.
*** [ DIAGNOSING ]: lighttpd version
[✗] lighttpd version could not be detected.
[✗] tcp:*:80 is in use by apache2
*** [ DIAGNOSING ]: Pi-hole processes
[✗] lighttpd daemon is failed
If this is intentional and you want to use only Apache on your system, you will need to configure Apache to run the web interface (with PHP).
Otherwise, you will need to execute pihole -r to repair the installation, to install lighttpd.
You will also need to change lighttpd port (or disable Apache) to avoid conflicts.