I'd imagine it's not bookable with Avios. I believe you'd need an AA stock ticket to be able to do that on the JFK-LAX route? It appears you're on a BAH so that means you're on BA tickets? You could pay for an upgrade at the airport, but no idea how much this would be, and as mentioned likely no extra Avios and TPs.
Answer to question 2, almost surely no. You'd be trying to pay BA for an AA-handled service. Happy to be corrected