Edit: I apologize for how long this became, but I was really behind on this thread and just started typing. Go ahead Tuco, give me shit.
Most/all of this is just political maneuvering. If it wasn't for NK making all of their recent threats, it is unlikely that we'd be able to mobilize all of this without a metric fuckton of griping from China. They don't want to see us deploy more assets in and around the area, but they can't really object too strongly (or at all) with NK saying all the shit they are. I'd put money on Washington knowing all of this and fully taking advantage of the situation.
No, the only response to a nuclear strike is the same, that is what keeps it as a deterrent to use.
Maybe if they had an actual stockpile of delivery systems that were proven to work en masse, and warheads advanced enough that they could actually fit them on a missile, then sure - but then we'd just be in Cold War 2.0. But I don't think NK is close to having that at all, and it is actually very likely that their launch would either fail, or even if it was successful, that they wouldn't be able to replicate that feat. In which case, once the damage is done, the decision to nuke them in a retaliatory strike doesn't seem such a sure thing. The world could instead say no to a retributive nuke strike, and instead see a vast military undertaking via conventional means to dig NK out before they could put together nuke strike #2. I could see an argument for a nuke strike in order to save lives in the event of a land invasion of NK (similar to the nukes used in Japan over the fear of that invasion as well), and I wouldn't be surprised if it were to come up for public debate. But honestly, this is all theorycrafting anyways, and I don't think that NK has a deliverable warhead to begin with.
Yeah, conventional is the way to go.
Drop some HAARMS do disable their AA and radar systems (we upgraded our HAARMS in 2010 so now they can still destroy a radar site even after it goes "dark" and they hear "MAGNUM!" over the radio and shut off the radar.) Then you send in the bombers and level the shit out of all industrial sites and military interests.
Oh there is no doubt that we could rape their air defense and static, non-hardened sites (hell the AF can fly over the effective ceiling of most of their air defenses anyways), it's the land war slogging through rough terrain fighting scads of crazy North Koreans (and potentially Chinese) that actually worries people. Maybe we could bomb them into surrendering, or cripple them enough that our losses on land are minimal, but honestly I wouldn't put money on it - and we can't know that for sure until it happens. They've spent decades digging in and hardening defenses. Remember how amazed we were to find out how extensive the tunnel systems really were in Vietnam? Now imagine NK doing that for decades in peacetime with actual construction methods. Sure, most would be strongpoints and bunkers, but you can build a lot of that stuff in 60 years with a captive populace.
That said, using nukes for any reason is never desirable, but if you are not willing to use them vs. powers that are, then it's not a deterrent and you might as well get rid of them.
If NK actually used a nuke, then the deterrent already failed, otherwise they wouldn't have used a nuke in the first place. At that point it wouldn't be about deterrence, it would be about retaliation. Sure, you could argue about needing to retaliate in order to deter OTHER nations in the future, but I don't think it is a cut and dry issue. The question is really whether NK is a rational nation just spewing bullshit atm (and therefore well aware of the potential repercussions and not about to see things through) or if they really are at the point that they are batshit crazy and feel that it's more important to fight and die than to submit to the West (as we thought might happen with Japan). If it's the latter then deterrence might not matter, and we'd have to decide if we were willing to turn the entire country into Fallout 4.
TL;DR deterrence will only really work when people are on the same page mentally - if they're willing to die to the last man and think that anything less is a sort of surrender, then you could have a million nukes ready to drop on them and they wouldn't care at all, deterrence be damned.
The one scenario I haven't heard the media put out there is that this is all being done to cement Tubby as de facto ruler not to his own people, but to the outside world. They don't need to rattle their sabre so much for internal reasons as for external. Think about it - as soon as he was to come into power, the rest of the world was positively abuzz over the implications. Meanwhile, NK wants to keep the status quo and stamp out any idea on the part of the outside world that peace is a possibility or that NK might have a softened stance. So queue this amazing amount of rhetoric and brinksmanship to push the rest of the world away so he can then sit back and rule NK until the next generation, possibly. The only danger I see with this, is that the rest of the world takes NK at face value (or pretends to, which is more likely) and decides to kick off a war and end the NK threat once and for all. We saw this happen with Saddam and Iraq (
"oh fuck, the Americans thought I was serious?"), hell Israel did similar when Egyptian forces crossed while the Egyptian president was on the batphone telling Israel that it was just for show and that he was posturing - Israel said fuck it, took the initiative and raped them anyways. Not that I think anyone has the balls to invade NK currently though, so it's unlikely, but I think that is what NK is banking on anyways - that they can push the rhetoric to the limit and he literally becomes entrenched as the next Great Leader, the West ends up shitting themselves over the possibility of war, and they end up getting offered deals so that they'll come back to the negotiating table. Chance of NK actually doing anything has to be almost nil at this point, unless we do something stupid to make them think that we're actually calling their bluff.