Its a 2002 audi A4, the mis firing occurs when am driving, and the vibration occurs mostly when the car is in park or I stop on the road

the only thing i can think of as a problem would be brake pad quality. i would get some from the dealer and fit them. if there is chatter going on it can also be caused by low quality rotors or a bad maching job. have them inspected for integrity.

This is a manual transmission? If so the clutch probably needs to be replaced. When you say "VIOLENTLY" what is going on, what is the road speed, what are the RPMs at? The more specific information the better. And this problem ONLY occurs between gear changes, right? The other times, everything is normal?

2002 a4 try fuel cleaner first, see how that goes after driveing for a while,,,the same goes for the 200 a4,, then we work from there

Does the humming noise only occur in a certain gear(s)? does it go away whilst changing gear or cornering?

check out harmonic balancer .

HI,IT SOUNDS TO ME LIKE THE TORSION DIFFERENTIAL ON THE GEARBOX IS CAUSING THIS,PLEASE TRY THIS,DRIVE THE VEHICLE TO A OPEN AREA,YOU MUST PUT IT IN 2ND GEAR AND DRIVE IN A CIRCLE ONE WAY ABOUT 10-15 TIMES,AND THE SAME THING CHANGING DIRECTION,THE REASON I SAY THIS IS TO LOOSEN UP THE TORSION GEARS,PLEASE LET ME KNOW,ANDY.

I WOULD GO FOR THE FUEL INJECTOR ON CYCLNDER 2...IF YOU NEED MORE HELP GET BACK TO ME!!!

you might want to have the transmission checked

Could be a transmission issue. Did you hit any objects while driving ? Have you performed a visual inspection under your vehicle ? Have you checked to see if you have any loose vacuum hoses ? Any codes in your engine control module or transmission control module ?

ok your problem is that your brakes are under force you shold get new brake pads ok