So glad to hear you're enjoying yourself
Hopefully, I can help get you all fixed up in this post, but if you have other questions (or I don't help), just let me know...
For the send button, it looks like you're template's container for each article has the "Overflow: hidden" value set, which means anything going outside the content bounds will get chopped off. Normally, this is fine, but for the Like/Send buttons, which use a pop-up which happens to go out of bounds, that's bad. Can modify your template's css file (
www.geti.co/templates/j51_digitalempire/css/template.css) to remove this setting. At line 51 (in the .content section) remove the overflow tag altogether, or change the value from hidden to 'visible'. That should fix that issue right up.
For the Invite module, make sure the "Enable Automatic Resizing" parameter is enabled. That fixes the issue on many sites, but not all. If not, there's a similar overflow:hidden tag at line 213 which may help.
The Live Stream issue is likely (hopefully) an artifact of having a new FB Application. The issue should hopefully resolve itself in 2-3 days as your application is registered throughtout Facebook.
Hope this helps, but if you continue to have issues, just let us know.
Good luck,
Alex