You'll need to get a certificate of conformity from Audi which is free of charge.
email the address as below with VIN number of your vehicle, name and full postal address.
cocrequests@vwg.co.uk
If you've bought it with finance I'd recommend you speak to the finance company. Advise them the car isn't fit for purpose due to the faults. They might fight your corner to get the finance agreement cancelled under the terms of not fit for purpose. This will cause Audi to fix the car or if it can't relieve you of it.
Have you had a diagnostic check to see if any fault codes flag up?
When was the gearbox last serviced? If s tronic it can stop engaging gears if the oil is degrading.
Does the gear selector light up as normal?
The first one when illuminated turns off the tow away alarm sensor.
The second when illuminated turns of the interior alarm.
Not sure about the 1, 2, 3 though
I think it's an issue with the screen. You could try disconnecting it and reconnect it but I think you might need to source a second hand unit as the most cost effective option