Hi Emmanuel
Thank you. But...
The installation on
http://modx.onlinefactory.ch had no images (and will be deleted now). For not letting legacy date to have an influence I test-installed a totally fresh MODX (2.2.5-pl) in a totally new website with a totally new MySQL database and the only thing I did after installation was adding the Gallery add-on.
But I finaly have the solution for the problem. In a new MODX installation the permissions of the directory /assets are set to 777. My provider prohibits PHP scripts that are within directories with that permission. Well, one may ask if 755 would be more adequate. I wrote a bug request for that:
http://tracker.modx.com/issues/9177
I hope this thread may help others. Thank you all for your help.