Lazy Emu, you need to look at the AA earning tables for the carriers you are travelling.
AA Flights
BA Flights
QF Flights
watch the * points in each table as it could trip you up, particularly this one for your JFK/LHR on BA:
** Transatlantic flights to/from the U.S. are not eligible for mileage accrual.
and the double kicker on AA:
** Tickets between North America and
Europe, India, Asia and Latin America booked in O and
Transatlantic tickets booked in Q are not eligible for mileage credit.
(Therefore, you may look at switching to an AA flight, or the codeshare flight number,
not in O or Q class, to get 100% mileage - personally I'd go for the AA flight because by then you might be able to upgrade using your status, points/upgrades).
This will assist you in points 1 and 2 - particularly which fare you decide to buy. Not worth buying a no-earning fare class if you can pay a little more and earn 50% mileage or even 100% (as well as the q-points).
Point 3: you'll get something for nothing all right. Chicks for free - well, you'll have to organise that personally, I'm sorry (but status will help if you see one checking in for your flight and you can ask her does she want to spend the time waiting for the flight with you in your airport lounge and free drinks/eats)...
Point 4: Well, I would presume that you'd meet the AA Platinum Challenge (I haven't done any calculations as we need to know what fare basis you are considering ticketing), but certainly enough for you to get free flights. AA redemption rates for award tickets is much better than QF's. Check out the
AA award redemption chart...
You could only use the AA points on AA flights (or use your upgrades if you have hit AA Plat). I'm not 100% certain of this fact (having not experienced it yet, but we may in Dec/Jan durig our trip to USA/Jamaica/Canada), but another AA guru (well known to others on this board) tells me that they do have some discount method where you are using recently earned points. Again, I'm not sure whether it's true but I'm prepared to believe the source.
Tip for the day: a surface sector is known as an open jaw.