According to one of the agencies recruiting for them you will be on what they call "worldwide contract".
1) What are the rotations periods at Air Atlanta? i.e is it 5 on 5 off, 3 on 2 off or something like that?
Eventually you can chose the rotation that suits you better.
NOTE: I've worked at many places with rotations and understand management very often don't stick to it 100% (even 90% is lucky). Again its just the nature of contract or ACMI work, one can't expect a stable schedule.
2) Can one live anywhere in Europe? i.e do I have to move or can I stay where I am.
As long as it is accepted by the company as a gateway.
3) Lets say its 5 on 3 off, are those 3 weeks off paid a basic salary?
You get paid by the day, which means, you are not paid for the 3 weeks off.
Besides of the daily rate you get nothing else.
Be aware that my information is 1 year old.