Which courthouse in Georgia performs weddings an a Saturday?

You'll have to call up the clerk's office and ask them if their judges do Saturday weddings. Courthouses are closed on Sat and Sunday. You'll have to either change the day to M-F or find a judge who does Sat weddings outside of the courthouse setting.

In my state you have to obtain a license in the county one or both of you live in. Check the phone book for the listing to your local county clerk. That office can answer questions regarding your local area. In the same office you could probably obtain a marriage license and book a judge to perform the ceremony.

None that I am aware of. There are many pastors that will do a civil service on weekends. In fact if you are in Atlanta I would be glad to do it on a Saturday. For example in Cobb and Fulton County they do weddings twice a day Monday though Friday in the court house.