) and then FB.getLoginStatus(callback) doesn\'t fire the callback funct
I understand that this question is a little old now, but I ran across it searching for solutions.
Double-check what you have set in your Facebook app configuration under the section "Website with Facebook Login". The Site URL domain must match the domain your page with the FB.getLoginStatus (and other related auth Javascript) is served from.
After hours of struggling, I realized that I could not reuse an existing app configuration I had on a new server and had to create a new app to handle the website login for this new server.
The other answers are probably equally valid in your specific case, but since there may be others like me who have struggled for a while on this, hopefully this gives you one other place to check. Making a new app with the correct Site URL was the answer in my particular case.