Joe, your car sounds normal...this is how the 2.0T FSI sounds, a little like a diesel at idle. Mine sounded very similar when I bought it new, but now after 55K it sounds a lot quieter...if you don't have a check engine light and the car is pulling well don't be too alarmed.
That sounds normal. It's the direct injection that gives the fsi that sound. On my A4 the car did not have the belly pan and the battery cover when I got it. Once I added that the car became a lot quiter. The pan is actually called a "sound baffel" so I guess that's what they are supposed to do. lol Just figured I would mention it. I bet this holds tru on the A3 also.