Heathrow + the tube one of the slowest option for the city - takes around an hour 10. Stanstead has a connecting train service right into Liverpool street in 45 minutes. City airport is even better. Even Gatwick into Waterloo then the Waterloo and City line is faster than the tube from Heathrow.
Heathrow is the obvious choice for connecting flights (particularly Asia or transatlantic). For European stuff, the other airports are often better.
not if you're final destination is somewhere on the tube west of center (plus you don't have to wait outside for a connection.) perhaps the transit time if faster, but with exchanges and potential delays, the tube is better, especially if you're meeting at a restaurant/bat/club directly from the airport.