I have a few suggestions wichs hopefully will help you furter
I think you schould search the problem in the ignition system as there seems to be no igniton in cilinder 4, the unburned fuel could cause black smoke and probably causes the coughs and sputters,
maybe a stuck injector is overfueling the cil so much that there is no spark?, your spark plug should be able to tell.
Do you have no spark on cil 4, or is the cilinder overfueld or underfueld?
as for the ignition system the power resistor/ignitor module could cause this as it drives the coil packs, on command of the ecu.
The cas send the timing information to the ecu and could also be messing up timing >> and ignition
The ecu could be broken but I would first check the basic engine sensors
if you remove the coilpacks and disconnect the harness of the ignitor module, and remove the sparkplugs. When you crank the enging you can see fuel fumes / clouds comming out the cilinder, if this don't hapen on a cilinder there is probably a problem with te injector / wiring.
you can look at the spark when cranking but be carefull with firre, and be sure that you disconnect the injector resistor blok so that absolutely no fuel is injected. Safety first. I have seen a firre started like this.
This can give you an idea what isn't function properly.
And if you have a friend with a descent running gtr you can swap cas / ignitor module / ecu, 1 at a time to know what's faulty.
Good luck