Need my installation checked

Goetz,
Like buttons are tied to a specific URL. That can be your Facebook Page URL or individual URLs (articles, etc) on your site. There's no way to aggregate all the Like clicks from your website onto your Facebook Page, they are distinct counts.

For registration / profile import, can you explain more about what is or isn't happening? Are users able to login using their Facebook credentials, or are they not logged in? Are you trying to integrate with a 3rd party extension, like JomSocial or Community Builder, and the user's Facebook information isn't being imported into those extensions?

In general, for "Automatic" registration, go to the Configuration area of JFBConnect and set the "Registration Mode" setting to "Automatic". Then, make sure that the JFBC Authentication, System and User plugins are enabled.

I hope that helps get you started, but if you can let me know any more about what isn't working how you expect, we'll gladly help investigate.

Thanks,
Alex