The remap button allows your users to reconnect their Facebook account to a different Joomla user if they want. It can be disabled in the JFBCLogin module if you don't want to allow that.
Regarding your application, I think Facebook may have disabled your application, or it's not public in some way (in sandbox mode, perhaps?) If you go directly to the application page, it redirects you to the homepage of Facebook, which is obviously not correct. For testing purposes, I'd try creating another FB App and use that secret, API key and application ID in JFBConnect to see what happens. My guess is that it will work. You'd have to contact Facebook to understand why the old application doesn't work
Your application FB page:
www.facebook.com/apps/application.php?id=74564052123