Bruno,
We just got into the site, and ran into an issue we've never experienced before. For some reason, our call to Facebook is failing in a very strange way. We disabled this call (for the overview area only), so you can get in there. However, ignore the errors at the top of the page. The information being received from Facebook is correct your Site and Base Domain look to be setup correctly.
Although you can get into the admin area now, the same problem will still occur on the front-end when someone hits the Login With Facebook button. We're going to investigate further to see if there's known issues with your version of PHP or cURL. cURL is the PHP library that lets us talk with Facebook. Both are out of date on your server, but not 'really' out of date, so I don't think that's the problem. It may also be an issue with your server configuration in general, but just don't know yet.
We'll let you know what we find. Can you tell us what host you're on?
Thanks, and sorry for the troubles.