Let's say I've got a Facebook app that I use for Authentication of my Users (http://developers.facebook.com/docs/authentication/). My current Website uses the domain abc.com, I've set that domain and a corresponding redirect URL in the facebook app settings.
I've got some users on my site, with working logins.
Now I need to change my domain to xyz.com. Will this affect the login and authorization status of my users ? I.e. if they visit xyz.com after the relaunch, will they need to grant permissions to my app again ?
No they don't. I always develop locally (with Site URL: http://localhost/) and then just upload the project, change the domain and no re-authorization is needed.
But I guess all the "likes" of your pages will be lost (not sure if doing a 301 redirection will maintain the count but I don't think so).