Oh, i love to answe this...
1. YES, the answer to a choice is always yes. Lol. You must withhold GA state tax and employee submits a non resident tax form annually as well as their TX form. They will have to pay TX while they wait on their refund from GA.
2. GA, and reason is you do not need to register in TX to have an employee in TX working for you unless licensing is involved
3. You would apply to Austin (capital of the lone star state) on your own, but only if you the need to run two separate payrolls since you woukd end up fikiing dounle thenamount of state stuff
4. Not sure what you are referring to here.