"1)Does LAX (T4), BOS and LHR have elite security lines available?"

Heathrow has fast track security for 1st and business passengers only. Regardless of any airline status, you are not entitled to fast track if travelling economy.

"2)What AC (or OW partner) clubs I can use? I have time in BOS and LHR..."

At Boston the only one around is the AA Admirals Club. At Heathrow you have a choice of the Admirals Club at gate 12B or the , imo, fare superior BA Club Lounge at gate 12A

Dave