Davide,
Your application is setup just fine. There's a few problems I see in your Joomla configuration though:
1) JFBConnect doesn't seem to have the AppID and/or secret key set. On your website, in the HTML, the AppId for JFBConnect isn't being set, so that's a big problem and needs to be fixed.
2) You have 2 other extensions adding the Facebook Javascript library, which are causing conflicts with JFBConnect:
a) Your Gavick template - You need to disable the social integration in the template settings and remove the Facebook AppId as well.
b) Something else - I'm not sure what, but right after the opening body tag is another inclusion of the Facebook Javascript library. This could be a module or plugin.. but it will need to be removed as well.
Our Autotune - Error Checker tool should show warnings about the above as well. Once fixed, it will show a "Pass" for all sections.
Let me know if that helps, but if you remove those and things still don't work, we'll gladly help.
Thanks,
Alex