The window is now ok with 4 rows, except on internet explorer. Thank you anyway, it parly solves the problem.
I see you are really struggling with this window, thanks for your devotion.
About the issue of the invite module which could not be clicked if a fan box was there. Actually I can't reproduce it anymore now. So you can forget this issue.
But a another worse issue happens :
When both the "invite module" and the "fan module" are there on IE8, the facebook connect button doesn't even show up, only the label is there, as you can see on this screenshot:
www.picturze.com/a/button_disappear.jpg
I send you the login and password to my test website by private message