Last night before early flight from LHR
 

We plan to spend our last night at a hotel near LHR because our flight leaves at 8:20 AM - American Airlines to DFW. So a couple of questions:

1. What time do we need to arrive at the airport for an 8:20 am flight?
2. Do all American Airlines departures leave from Terminal 3? Need to figure that out so we know which hotels are closest.

Thanks in advance!