When I did my stage 2 I had to go out past the barriers to smoke...in the rain
but at heathrow it's over a mile to get out of the airport and then you'd have to go through security all over again!
As for stage 1 I didn't answer a single question on the 3rd cube, time had run out just as I was working it out and I still got through. So there is hope. I think accuracy is more important as long as you answer an unspecified minimum number of questions.
Because this thread is so long can someone point me to where I can get info about what to expect from stage 3?