Well the A3 was the first car in the VAG to use the "a4" chassis. (which is in the TT and golf) so that suggest to me that Audi designed it.
No, it doesn't. AFAIK the platform name "A4" has nothing to do with the Audi car. It means 4th generation A platform - the A platform is the platform for compact cars car, the B platform for midsized cars and so on.