I replied inline

* Is it the .basex file which is located in "C:\Program Files (x86)\BaseX" ?

No, it's located in C:\Users\user\.basex

* What happens if you start the start menu shortcut "BaseX Server (Start)"?

C:/Program Files (x86)/BaseX/.basex: writing new configuration file.
HTTP Server was started (port: 8984)

Now it works fine