like button and comment box errors

Matthias,
Try using the Facebook Debug tool below, to see if it can see your site properly:
developers.facebook.com/tools/debug

Usually, if this is a brand new domain, Facebook may not recognize it for up to 24 hours, as it's never seen the site before and needs to do some checks for spam, bad content, etc. If that's the case, it will clear itself up on it's own. Alternatively, make sure you don't have a password protection on the site, or other things that would prevent Facebook from seeing the pages on the site.

If not, we may need to see the actual URL for the page to diagnose it further.

Thanks,
Alex

Yes, if your site is offline, Facebook can't see the page. Once it sees a few pages it will be able to determine that your whole site isn't spam, porn, malware, etc. Once that happen, pages that require registerion (or if you go offline altogether again) will be ok from Facebook. They just need to see a little of your site first.

As for the comments module, it's not installed by default. It's part of the social_modules zip file that is in the download area. However, without the comment module, you can still use the Content plugin (installed with the main component) to automatically insert the comment box in articles or the {JFBCComments} tag to do it manually.

Hope that all helps, but if you have other questions, just let us know!
Alex

P.S. Great avatar.. had to take a picture with my phone, then translate to English.. but quite amusing.