Welcome to the forum you'll find the members on here are a friendly and helpful bunch 🙂 nice looking car 🙂 you'd be more than welcome to come along to the shows with us. Our next show is Das Auto show at Santa Pod this Sunday.
If you got it on finance speak to the finance company telling them it's not fit for purpose. But if Audi can't find the fault then you're in a catch 22.
It would need coding and fitting professionally. I'd recommend you'd speak to a retrofitted such as autologics. Think you'd be looking £600-1000 to have it fitted. You'd be better off getting an A3 that has it fitted already.
If most are in town then I think you'd be better with petrol to be honest. Regardless of engine make sure the gearbox has been serviced on time and that the tyres match/say tread as uneven tyre wear can damage the quattro system.
I'd recommend a diagnostic check to see if any fault codes are stored regarding the start up issue. Sounds like it might not have been running on all cylinders maybe?
Regarding air suspension is think level 2 is standard. Wouldn't 1 bar be dynamic and 3-4 off road etc.
The question what s, how many miles do you do a year and what kind of miles. If it's low miles mainly around town then avoid diesel as you'll just end up with blocked egr or dpfs.