Also... three hours is plenty of time.

Yep, if you're all booked on a single QR ticket then let of the deal is through check-in.

Is your VA flight on the same booking? If so it should be checked all the way through. If you've made it separately then no. Alternatively if you can cancel VA flight and book a QF award flight this would normally be checked through to your final destination. Can I ask if you didn't book all th...

Use the QF First Lounge. You can access airside AA domestic gates from the Tom Bradley Terminal via the link way. Just allow a reasonable time to walk depending on which terminal you are departing. Most go from T4 so not too far.

A Qantas flight whether it's domestic or international, in my experience is credited pretty much after departure, so should be ok.