Ok i think i know what your problem is....
When i check your source for homepage and forum i did notice one interesting thing....i actually think this plugin IS working for the homepage but found nothing to minify. Here is what's going on:
All your js/css files on the homepage (and most on the forum) are files located on your CDN (and a few on Google). This plugin will only minify, by default, files that are on your local server at teatra.de. So you have to add any domains (partial matches are fine) that are not local (i.e., "teatradenetwork" and "googleapis") into the config admin page ("External JS/CSS Files") for this plugin -- 1 partial domain per line. This should resolve your problem. You can then set up your cdn to pull the newly created single cache file (js and css) back to itself so as to host it from there instead of locally (assuming your cdn is advanced enough to do that).
Just be aware though that i did notice you have some inline js code and am not sure if it is placed in certain areas for a reason which require specific js files to be loaded at certain times....by caching them via this plugin in one area (by default, at the top) you might need to be careful and might need to relocate the inline code before the cache file loads in if the code requires it to be done so (eg., some times people like to initialize variables inline before loading the required js file done after it).
Hope that helps.