Something is up with the 'Invitation Message' field..
On your demo site http://vanilla.stackideas.com/others/friends/invite
you can't enter anything at all (no editor shows)
(EDITED: I fixed the issue below on my site with these buttons - They were generated by default button plugins which I disabled)
On my site, you can, but MENU and CONTACT buttons show below it and seem to give users access to things I'd only want ADMIN seeing
(this now fixed, but issue remains as reported above on your demo site)