This is as designed. Transmission will jerk. In terms of downshifting it's best to allow the car to do it itself when you get from 3rd down to 2nd (and eventually 1).
As far as other jerkiness, that is also a "feature" (
) of the car. Latest software revisions make this jerky acceleration in 1st less than it used to be, but still requires a bit of throttle modulation. Take your time and get used to it, and make sure you have your seat at the correct distance from the pedal.
Even in Sport+, S3 I rarely if ever have issues with jerky acceleration.