I just did some more testing. You definitely have some sort of restrictions on your app, somewhere. If I try to go to your Application Page on Facebook.com, I get a message "Use of app "ΕΛΕΥΘΕΡΙΑ ONLINE" has been restricted":
apps.facebook.com/eleftheriaonline/
If I go there when logged into Facebook, it works fine.
So somewhere in your Application settings there is something that is denying non-logged in users or users that aren't from a specific region or age group. I'm not sure what it is, but this is not being caused by JFBConnect. Please go over your settings or even try creating a new FB Application and test if using the new App ID and Secret keys causes the same problem.
Thanks,
Alex