Yout bags will be checked through to your final destination - no need to collect them at London

Since you are departing from Terminal 5, I do not think that you will have access to Terminal 3 departures and the lounges there. You will be able to access the AA Arrivvals lounge in T3 ( if you choose to clear customs/immigration and go landside ) and to the BA lounges in Terminal 5. Since you are arriving into London in 1st class on AA, I believe that you will be entitled to access the Concorde Room. You definitely have access to the 1st lounge and the Club lounges

Can you not get a connection that is better than 6 hours? that is a tedious time to spend at an airport