There is also the MARTA train directly from ATL that stops at Peachtree Center across the street. It is definitely faster than a car if there is any traffic, which is often in Atlanta.
Unfortunately No. You will likely want to take an Uber or Lyft
Not that I'm aware of. However, as mentioned, there are many transportation options.
The hotel does not provide any shuttle service but there is the Marta that goes directly to the airport and there are plenty of taxis that are available at all times at the hotel
I took a cab because it's in the flat rate zone, however an Uber or Lyft might be cheaper and as Christopher said, the MARTA train stops at the airport and has a station in Peachtree Center which is pretty much under the hotel.
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