Yes, I have done it a few times.
state where vehicle is registered
Texas, the state of your residency
yes
Yes, it is possible to buy a car from a dealer in one state and pick it up in another state from a dealer of the same car company. Although this transaction might be unusual, it is possible. Shipping charges might apply depending on the situation.
Sales tax on a car in Georgia is based on the county you live. Does not matter what county you buy it in. If you live in another state and buy the car in GA some dealers will not collect the tax for your state. However when you register the car your state will collect the taxes owed.
You should be charged the sales tax from the state you live in. I know that if you live in NH and you buy a car in another state you aren't charged any tax because NH doesn't have tax.
No, you must change your car insurance when you move
Yes, The insurance of a vehicle has no bearing on where the car is purchase or register.
No, you would need to register it. The dealership simply "signs off".
You can buy a car out of state in any state in America. However, you must transfer the title and paperwork and license it in your state.
Yes. There are interstate commerce laws in place so that you may purchase anything from another state legally and import it into another state.
either buy check,cash or money order. but also if you are selling it to an individual from another state a person could get it titled in that state for a fee.