will 15" rims fit my a3?

If they fit on a Mk5 they should fit on an A3. They won't fit over 3.2 or S3 brakes, not 100% on the size of the standard discs/calipers.
 
Oh I thought the smallest you could go was 17? Because the front brakes would not allow me to fit a oem spare tyre, only the back would.
 
Well after a bit of research I can semi-safely say they'll fit. The most easily searchable car that runs 288mm discs (like those on the 1.9 TDi A3) is the Mk3 VR6 and they can run 15" wheels so you should be ok. You should double check the offset though, since there'll be very low clearance.

17" is the smallest that'll clear the S3/3.2V6 356mm brakes, maybe that's what you're thinking of Snipe.

Just as a 'get out of jail free', this is based entirely on internet research done at 2:30am and in no way should be held as gospel.