I have 96 JDM integra type R and I'm currently having a few problems with it.

1) When the car is first started it doesn't really run on cylinder 4 but as soon as the car starts to warm up it will run reasonably well on the cylinder.

2) All the plugs are fouled with carbon and the car has a bad miss, even when it is warm.

3) The engine will splutter when it is trying to idle. The engine will be idling at 900 revs then it will drop down to about 300 revs. It generally does it after a load is taken of the engine i.e. turning the steering wheel or taking your foot of the gas pedal.

So far I have changed: iacv with a know working one, leads, distributor cap, distributor rotor, spark plugs, fuel filter, map sensor and checked the cambelt has the right timing.

Are all these problems related? What else should I change to try solve the problem?

Videos of the idle problem:

 

check your compression in all 4 cylinders....
check your fuel pressure as well...not enough fuel pressure can cause a miss...but usually a more consistant miss
the plugs being fouled with carbon leads me to believe your burning oil...this is more than likely the misfiring issue you have.
for the idle issue - try calibrating the TPS with a multi meter - i dont know the exact specs, but im sure you can find the procedure on this site somewhere
check carefully for vacuum leaks - this will also cause a poor idle

 

make sure if the ignition 16degree on idle...