The experts on this forum will no doubt tell you you are better off booking through AA than QF, and all I can do is tell you of my limited experience. QF charge a fuel levy for outbound international flights from Sydney, and when I recently booked a return flight from SFO to SYD I was not charged the levy on this leg as this was a separate one way booking through www.qantas.com (not .au). However, I was charged the fuel levy on the outbound leg from Sydney and it may well be that if you book through AA you would not pay the levy in either direction. Other will correct me if I am incorrect..

I don't have the experience to assist with your questions 1 or 2, or whether you can transfer the points from BA to AA etc, but it cost me 96K QF ff to fly one way SYD to LAX in business, so you might be able to work something out from this on the AA site.

Edit: There you go, tinkybelle is the first to the rescue already.