On your dev site, open up the html and look for 'all.js'. That's Facebook's Javascript library. Before the all.js in the URL should be the language of the library that's being included, and that's set by your Joomla language setting. The all.js file should only be loaded once, by JFBConnect. If you find it multiple times on the page, and with multiple languages, that's the problem.
The new invite module is still in planning. There's a few other features that need to be implemented first, but hopefully, we'll be devoting some time to it for the 4.0 release in July. Generally, when we say the 'next' release, it's either a minor (3.x) or major (4.0) release. The release that just came out (3.2.2/3.3.1) was a bug-fix/minor-feature release which we do about every month to clear out any issues we can or implement minor new features from Facebook (like the Send button in this latest release). Just writing that out, I can see how that's confusing
Hope that all helps, but if you have other questions, just let us know!