Hi,
The
HM Revenue and Customs website is a useful reference for Air Passenger Duty (APD) information.
Based on the information on the site, in regards to your questions my understanding would be that:
1) if you are connecting (outside UK) -> LHR -> (outside UK) on a single itinerary within the allowed connection times, no APD due
2) the duty applies to 'Air Passengers on Chargeable Aircraft', not to train or bus journeys. Coming back from the 'third country' (outside UK) -> LHR -> USA, no APD due, same as above.
Cheers,
J-