Since you are flying "internationally", AA allows 2 pieces of checked baggage of 50Lb which is exactly the same as allowed by Qantas, so you will not be allowed any additional baggage. You wont be chaged the domestic baggage fees

2hrs 27 is ample time. On arrival at LAX follow the signs for the Qantas TBIT flights and I think that there is an airside transfer to the other terminal


On the way back, 2hrs 20 should be enough unless you are unlucky with queues at US immigration. After immigration, collect your bags , go through customs anddrop off your bags . Then exit the terminal , turn right and walk about 200 yards to T4 and head through security

Dave