One, how much "throw weight" does the system have? That is, it can boost a small satellite to sufficient altitude and velocity to achieve orbit. If you increase the payload weight for say a first generation nuclear bomb, that's a lot heavier. So it probably has enough total energy (impulse) to throw that kind of weight in a sub-orbital trajectory. How far? A related question is, just what would a first gen RV and warhead weigh?
Two, what kind of accuracy could they place a warhead with? A small fission device of a couple dozen KT, although a good terror weapon, does have a limited effective radius. If they aim for a city, it's probably going to be harder on some of the suburbs... Then again, maybe they just go for an EMP weapon and detonate exo-atmospheric over the central US or the city concentration on one coast or another?
Three, what kind of reliability could they achieve? An ICBM flight is full of engineering challenges, heat, cold, shock & vibration, supersonic airflows, solar radiation... It takes some real engineering to get the components of a nuclear weapon to survive that. It isn't the same as a simple science project in a cave.
So yes, they have a budding nuclear weapons program. They have a vehicle, it can hit us, but with what and where and how much is the question. Then there's the little thing of the several dozen missile interceptors sitting in Vandenberg and Greely. Our radars see something on a ballistic trajectory rather than an orbital insertion trajectory...
We don’t have radar looking south, and NK’s 2 satellites have both been put into a polar orbit which would allow them to shoot at us from the south. Their satellites are both at the precise altitude for an EMP attack. Both satellites are tumbling now so if I understand correctly, they can’t hit us with an EMP that way yet, but as soon as China wants the trigger-happy Kim Jong Un to have EMP capability they can put a satellite into orbit that doesn’t tumble.
Correct me if I’m misunderstanding.