Sport has lower/stiffer suspension, different wheels, 3 spoke steering wheel. I think SE may come with cruise controll too (does on the 8p). Theres a few other subtle differences but cant quite remember them at the moment.
Do you not need a windback for this? I got stuck doing the missuses golf one sunday, got the pads out and couldnt push the pistons back, then couldnt get the old pads bak in to take it to the garage. Ended up having to use a set of mole grips and a metal bar to push and wind.
Not trying to put...
Possibly an intermittent fault with the brake switch under the pedal. I had one go on my first A3, I think its quite common. Cheap enough for a new switch though, I think there about £15 ish.
You might wanna get someone to check your brakes while you pumping the pedal.