No state has a requirement that you be a resident in order to buy property. Some states may require you to be a resident in order to get preferential tax treatment (such as being 'homesteaded').

Sure you can.

You would not be required to be a resident.

Yes you can.

IMO, Tennessee has great weather! Warm & humid during the day, but cool at night.

Of course you can buy a home there. WIkipedia is your friend

You do not need to a resident in TN to buy a house there. As to your other questions, I do not know.