Open-carry is a fools game. Never do this. Get a CCW, and keep your weapon out of sight until you need it.
Yes, with a valid gun carry permit (Georgia Firearms License or now it's called a Georgia Weapons License), or with some other state's permit that has a reciprocity agreement with Georgia, or if you're exempt from the permit requirement by holding one of the government jobs listed in 16-11-130.
Banks are like shopping malls and restaurants and office buildings and other private business property. They can make a "rule" that says no guns, but it's not a law. Just like they can make a "rule" about no gum chewing or no Skateboarding in the parking lot, but it's not a crime unless they ask you to leave and you refuse or argue with them. (THEN it would be the crime of criminal trespass).
You can't carry a gun in Georgia without a permit.
It is legal to carry a Taser in a holster or purse in Georgia.
You can carry a gun in TX if you have a permit
Depends on where you live.
With a license, yes.
Yes
with a permit, yes.
Yes, it is legal to carry a gun in a bank in Tennessee as long as you have a carry permit. In TN however, any business can choose to post a sign banning handguns on they property, and a few banks have done that.
I hope so.
No
No. You can purchase a gun from a Georgia dealer, have it shipped to an FFL licenced dealer in California for receiving, and receive it in California, but you can't purchase a gun in Georgia and carry it with you as a California resident. This is due to California's laws, not Georgia's.
You need to consult a lawyer familiar with firearms law in Georgia.