1. Yes, the tier points and Avios will credit to your BA account as long as you enter your BA number (and no other frequent flyer numbers).

2. If booked on aa.com, you will only see the booking on the BA site if there is a BA flight (or flight number) somewhere in the booking. If all AA flights/flight numbers, you won't see it on the BA site.

3. Once booked on ba.com, go to manage my booking. For AA-operated flights, when selecting seats, you will be brought to the AA website. You will then be able to select Main Cabin Extra.