Most likely the IAC is getting stuck. Replace the IAC. When replacing the IAC, it is usually a good idea to clean the throttle body first so the new IAC lasts longer.
Speed Sensor is not working
Try adjusting the idling speed - sounds like idling speed is too low so when you take your foot off the gas it can't idle (Tick over)
Where the passenger side CV axle enters the transmission.
The Z24 has overdrive, the base models are 3 speed autos
The automatic transmission in the 1991 Chevrolet Cavalier is the Turbo-Hydramatic 125, and was later renamed the 3T40. It is an automatic 3-speed used in similar j-body cars of the time. Source: http://en.wikipedia.org/wiki/Turbo-Hydramatic_125
The idling speed is automatically sensed ....and set by the Air control valve
It is zero: when it is idling.
yes
3.5 to 4 quarts with a filter change on the 4 speed auto.
4 speed automatic.
Kinda need more information. Is it just when accelerating, or also when idling in drive? Does it only do it at a certain rpm or speed, or when applying brakes?
sounds like the speed sensor. it sends a signal to both the speedometer and the transmission