Sorry, but that black stuff on your plugs is not carbon. Well, it is, but not of the kind that the term infers. It's oil fouling, and it means your car is done. That is a $500 car, and if you dive into the engine, you'll be flushing money down a black hole. You'll be MUCH better off using ANY money you are thinking about spending on this car and either buying something newer or using it as a down on a better car.
Drive it until it fails completely, which might be months or a year.