For the email invitation, you may want to try the following modification to the JFBCInvite module. I'm not sure if Facebook changed something, but that setting is still available to use. However, we set it to '0', whereas they recommend 'false'. To make this change, open the /modules/mod_jfbcinvite/tmpl/default.php file. At line 58, you'll see where the email_invite parameter is set. Change this to:
Hopefully that will fix that issue, and if so, please let us know!
As for the resizing, I see the Javascript we use trying to execute, but it's not catching the event properly. Can you try changing the setting for number of rows to a lower number (I think you're at 4, so try 3 or even 2), and see if that fixes it. If so, hopefully that will be acceptable for you, if not, we can investigate further why it's not resizing properly.
Thanks,
Alex