The Bodykit was a factory option Nismo kit you will see a fair amount of 34's with the same kit and that is why, although not so many of them have the huge wing.
Your other problem sounds a little strange to me when the coils go in my experiance i have never had the engine check light come on and usually it will miss in any gear when you start to load it up on boost, also once they coils start to go they usually don't come good again just because you restarted it. what boost is it running is the car 100% stock?
The other guys on here may have heard of this before i will be interested to find out what the problem is. Unfortunately it is a pretty common problem with Skylines having coil pack problems have you had anything done to it like new plugs etc since you bought it?