Let us say I have got a Facebook application which i use for Authentication of my Customers (http://designers.facebook.com/paperwork/authentication/). My current Website uses the domain abc.com, I have set that domain along with a corresponding redirect URL within the facebook application configurations.

I have got a bit of customers on my small site, with working logins.

Now I have to change my domain to abc.com. Will this modify the login and authorization status of my customers ? I.e. when they visit abc.com following the relaunch, will they have to grant permissions to my application again ?

Does altering the website URL/Domain of the Facebook Application affect your customers?

No they do not. I usually develop in your area (with Site URL: http://localhost/) after which just upload the project, alter the domain with no re-authorization is required.

However I guess all of the "likes" of the pages is going to be lost (unsure if carrying out a 301 redirection will keep the count however i don't believe so).