I get a discounted BA rate through FC of up to 10% off. I found an AA flight on there, that saves me about $25 vs. AA's portal. A few questions:

Would the EQDs code equally, even if it was discounted?

I can also use Avios to discount some of the booking, potentially getting about $64 for using some useless 6k Avios: would that also affect the EQDs?

Finally, in the case I use Avios as said above - how do I make sure this flight codes/counts for AAdvantage, and not BA Exec Club?

EDIT: Found on FlyerTalk that if flights are booked through a codeshare, to use the codeshare award. If they are discounted, then it shouldn't matter if it goes by distance, right?