When I first start the car I do notice white smoke, and the whining noise does sound like a siren.

 

Based off the information you are providing us. I would say its the turbo. Take it in to a reputable tech and have them properly diagnosis it.

If it's bad replace them with RS4 K04's. Your mom will love it!

 

Suuuuure. I never go to full serve. I was a gas jocky for 3 years of my young life and would never subject someone to that crap job.

No I remember it was the pump. I selected premium and it hesitated. Pressed the premium button again and still nothing. Finally the pump make an odd beep noise then allowed me to select premium. Faulty pump for sure.

The girlfriend drove it nice and girlfriend like on the highway, never passing, driving like she does. That got it down to 1/4 tank. Filled it with Shell V-Power 91 octane and the problem instantly went away.

Bad pump. Never going to that gas station again.

 

Man, low octane gas would NOT cause that. My A6 had no other signs except for being "sleepy" when accelerating. As the mythbusters would say, "Smoke? Noise? Well THERES your problem!"

 

Also if you can put the car up on a lift take off the belly pan and remove the lower boost hoses to the the right and left of the oil pan. See if you get any oil out of them. A few drops is ok but tablespoons are bad. The 2001 / 2002 had alot of turbo problems because the oil line gummed up. They fixed it for 03 / 04. I just had mine replace a couple of months ago under warrenty. It would have run 4500. The have to pull the whole motor out. Its a big job. When you are under the car looking towards the front, stand at the front cross frame rail and look up to the left and right, Thats where the turbos are.