It doesn't have to be on a warhead but smuggled somehow.
It would certainly be traced back to them so I don't think they will ever target America directly.
While this is possible, it's clear that this would be a deterrence first. The point would be that minor strikes or political actions would not have a much higher cost. For example, North Korea does not want to nuke the US. They want to possess nukes such that US actions are more constrained. It's a very unfortunate incentive.
While I agree that the main point is deterrence, the rules have changed in the last 50 year and it's not always a country vs country. Israel created their nuclear program to deter an all out war that could lead to Israel destruction but today Israel isn't fighting their direct neighbors in a conventional warfare.
Nukes in the hands of North Korea are bad no matter what, don't underestimate a mad man and their cult followings.
? Target anyone at all with a nuke and you are getting invaded by an international coalition at minimum and quite likely nuked yourself.
Maybe, maybe not. Once you have shown you have the capabilities it's a different story, but then again you don't have to directly do it, just leak it to your "friendly" neighborhood terrorist group and let them take the blame. Maybe Iran is a different story but what if a dirty bomb was made from India's or China's nuclear materials for example, would an international coalition invade them? I doubt it.