Mike,
Step 1
For "I've used the redirect option setting after logging in", what setting specifically are you talking about? For Facebook login's, the redirection is completely configured in the JFBConnect component admin area in the "Login/Logout Redirections" tab. The JFBCLogin module only has a redirection setting for users that login with their Joomla credentials.
In the login redirections area, you'd want to disable the "New User" and "Returning User" login redirections. That will always leave the user on the current page, which in this case, would be the Invite page.
Step 2
I'll have to investigate, as some things have changed with how we should be checking if the user is logged into Facebook in JFBC v4.0. We didn't make any changes in JFBCInvite, and didn't think any were required, but it's possible we missed something. However, we're not seeing that issue when not logged into Facebook on our demo page:
www.sourcecoast.com/jfbconnect/demo/jfbcinvite-module
Could you check that link and see if you see issues? Also, if possible, can you post (or private message) us a link to the page with this issue?
Thanks,
Alex