Can you please help me with my flight connection and what to expect when flying from JFK-LHR on AA and then four hours later from LHR-FCO? I believe the AA flight arrives into terminal 3 and the BA flight leaves from 1. A few questions:

Can we check our bags through to FCO all the way from JFK?

Once we arrive in LHR, how do we get to terminal 1? I would assume we have to clear customs.

I know the restrictions on carry on bags is tighter leaving LHR. What happens if our computer bags are slightly too large? I have a targus computer bag. Is that too big?

Is there a BA club in terminal 1 we can use? Showers?

Thanks for the help.

Mike