Check the shop manual for your car. Every car has a limit as to the highest rpm the engine will go before it stops. It is a safety feature. 4,000 rpm sounds a little low, but it could be correct. Normally, it is higher. If it is higher, you either have computer problems or a broken wire or a wire with a little insulation missing.
Yes
Yes
Yes
The engine has a rev limiter while the transmission is in neutral. It will rev to higher rpm's when the transmission is in gear.
you need the fast idle adjusted on the engine you may have idle set where it sounds fine in idle but not high enuff when dropped in gear.
Could be throttle plate stuck open Try to free it with screwdriver with engine off
check the soleinoid
The engine idle may be set to low to compensate for the AC compressor starting up. Rev the engine a few times to see if it stops. If it doesn't, there may be a problem with the AC temperature signal or motor mount.
If a Zx2 shudders and dies out at stops and idle, the idle might need adjusted. If the idle is set too low, it will not maintain enough power.
If it is running fine at high revs the most likely problem is an injector
if you do have gas in the car then it could be the idle control valve. it stops the engine from stalling when the car is stationary
The TURBINE inside a turbo-charger stops spinning when the vehicle is at idle because there isn't enought exhaust pressure to keep it spinning, lowering the internal engine pressure. creating less wear on the turbo and engine also alowing the engine to idle.. if it was to continue forcing air into the engine it would also need to force gas. to match the air fuel ratio to keep the car from dying, causing the engine to rev.. not stay at idle..