@Kristian Gettemy
Welcome to BP. Investing here from EU will likely be a little more challenging than if you were local here, but it's certainly still worth pursuing, I think. To answer your questions the best I can:
1) you might want to consult a lawyer in GA about possible complications with opening an LLC from abroad, but yes I would look for this as a first step if I were you. Let me know if you'd like some lawyer recommendations here.
2) if you can find a lender (either in Norway or here in America) that will lend to you for your LLC, yes that would probably be the best route. Otherwise you'll likely either need to find an American partner or pay all cash.
3) turnkey would certainly be easier for you, especially from a long distance, but you'll be paying a little more in exchange for the ease.
4) most areas of GA should generally cash flow reasonably, but as a rough rule of thumb, the farther from Atlanta you are, the better your cash flow will likely be.
Feel free to reach out there's anything I can help with. I'm a local investor and agent in Atlanta. Always happy to talk about the market here.