Not sure if you still need this info, but if so, we are at Paddington pretty frequently. I don't recall that we have used a lift there - I think it is just escalators.
RE: the tube station accessibility - anything with Jubilee line going through it has lifts, in my expereince (I am usually pushing a stroller so am always aware of which stations I don't have to deal with stairs).
RE: the Tube service to Heathrow T4 - don't mess with the replacement bus service from Hatton Cross like they tell you to. Just get off at the other tube stop. Then go in the terminal and follow the signs for Terminal 4. You can take a pedestrian subway with a moving sidewalk. We may have had to briefly get on the train, and then get out at the next terminal, but it was free. (Sorry to be so vague, the departure and arrival have blurred a bit in my brain). Anyway, I wouldn't rule out the tube to Heathrow just because of the replacement bus service as there are ways around it that are much easier to deal with.