1. There's no need to go to TBIT unless your flight is somehow routed there or the passengers are routed there upon arrival. However, AA192/193 seem to consistently arrive at and depart from T4.
2. Upon arrival at LAX from HKG, you'll clear customs/immigration and then drop your bag back with AA for the flight to IAD. Upon arrival from IAD at LAX on your way to HKG, you won't see your bag at LAX.
BTW - since you have so much time on your connection, you might wish to make the walk between T4 and TBIT to visit the Qantas F lounge with your OWE status. It's not far as it's the first thing you hit in TBIT when going through the connector. Also, AA193 usually departs from gate 41 or 43, which are also the first gates in T4 that you encounter after arriving from the TBIT connector.