Hesitation acceleration idle

I would check timing or spark plugs

Sounds like your spark plugs need replaced. ( long shot answer)

Is the check engine light on, and have you checked fuel pressure with a gauge ?
The most common cause of that problem is a faulty Throttle Position Sensor but it should set a code in the computer.

hesitation on acceleration misfiring, the engine idle is erratic and the cat gets cherry color,and at the back of the exhaust the emissions smell like a rotten eggs,always the idle is not steady .

your fuel injectors are clogged

i would try cleaning mass air sensor, its mounted in air duct between air filter and throttle body, they sell the cleaner at auto parts stores, also as stated bofore make sure the intake pipe clamps are tight and it's not cracked, if that doen't fix it i would investigate a fuel pressure problem either a weak pump or problem with regulator

My 99 Audi A4 2.8 Quattro was havinga problem starting at times. It would idle poor upon start and then it would come up in rpm where it should be. I had hesitation from a start and after coasting for more than 5-8 seconds, the car would shake violently upon acceleration at about 1/3 throttle. I cleaned the Mass Air Flow Sensor. This helped but did not solve all my problems. I then replaced the Mass Air Flor Sensor. Little to no change there ($108.00). Lastly, I replaced the spark plugs. I bought Bosch plugs ($4.82 ea.). This got rid of all the symptoms. I had bad lugs and possibily a dirty MAF!

it sounds to me that the sensor your talking about is the camshaft positioning sensor. It regulates how much fuel you get to your engine, so that is also why you have the fuel smell as well.

You more than probably have a gas leak somewhere in the fuel system. If you can smell gasoline, it is leaking somewhere. The lines run along the frame to the engine. The leak might be hard to see or hidden (on top of the fuel tank).

The leak is robbing fuel pressure from the engine, causing it to idle rough, so is probably on the pressure side of the system.

(Most fuel systems, except for "returnless" systems with Pulse width modulated fuel pumps (not very common), have a pressure line and a return line to the tank.

sounds like unburned fuel in the catylistic converter suddenly burning the fuel as your car picks up speed [causes the rotten egg smell] your hesitation sounds likley to be [tps sensor] throttle position sensor its a variable resistor which is known to breakdown not a difficult repair and can be tested on a multi meter with a bar graph on it yates210456