Used the Oyster card to get around, super easy. Got a refund for the unused balance at the end.
Took the underground back to Heathrow and I believe it was a straight shot from the Hammersmith stop.
I really like seeing Queens Guard but not everyone cares about that.
My general advice is pack light. A carry-on size bag is much better to manage especially on crowded trains.
At the Shepherd's Bush market there's a great samosa stand. Cheap and delicious, we could have gone there every day.