You can get original routing credit from UA. I don't expect you'll have much luck with the AA miles but you could try to get BA to enter you AA number on the reservation.

It would not have been possible for you to get into T2 departures. At T2 (as everywhere at LHR, for the most part) arriving and departing passengers are segregated. Without a BP for a T2 flight you would not have made it past security. It is as simple as that. What UA could have done for you (but probably wouldn't have) is give you a pass for the UA arrivals lounge outside the T2 baggage area.

There are no *A lounges at T3, but various paid options if you are so inclined.