I will need to book a one-way flight on BA in economy (paid) from LHR to Athens in September.

Will this include one regular checked bag?

Am I able to earn AA miles on this segment, and if so, is there a mechanism for entering one's AA Advantage number on a reservation booked on line from the US, or does this need to be done manually?

I also understand that seats would be assigned at the airport.

Any assistance will be appreciated.