Russian spy plane flies over Boston area

Eliminating the NK nuclear capacity could be quite readily done with relatively low risk (to the men flying the mission)

The consequences of that action are the true fear.

The door to this option is rapidly closing.

So we are willingly letting another country into the MAD game?

Talk about the height of foolishness.

1.) We don't know where all the weapons are. They could be buried deep in the mountains or set up to be moved around..

This isn't a problem with ICBM. The trajectories are easily calculated, knowing the target, they are not really a problem, ironically, the longer the distance, the easier it is to calculate the flight path. Real question is if he's really saying "I'm gonna hit Guam" does he mean it? I say it's simple...hit every missile out of DPRK. Over the ocean to avoid land based casualties. All missiles. Every shot. This sends the message that not only can we do it, we will do it. It also assures our allies that we can do it and will do it.
It also deprives their engineers of any telemetry they might gain.

2.) How do you destroy a nuclear facility without releasing large amounts of radiation? Do we write off South Korea?

You don't and you don't. They need missiles. Without a delivery system, they're hamstrung. Ox carts? Without missiles, the nukes are useless. The ROKs are tough, will fight back on any conventional attack. Don't sell them short.

3.) Even if they can't really retaliate against us, North Korea has the capability to deliver poison gas to Seoul and Tokyo.

Um...yes. Probably to some parts of Seoul, definitely not Tokyo. Poison gas is a game changer, like nukes. It means the destruction of the political base of the north. Also, what if the wind, a fickle thing, shifts? Stuff blows north, maybe? There's a reason no one used it in WWll.

4.) North Korea has a close alliance with China. If the "first strike" leads to casualties in
China itself, they may join in on North Korea's side. There are 2-3 million people in
the area around Dandong, the largest border city.

China is definitely NOT going to jump in. They will preserve DPRK as a communist system, we can't stop that, but that can be done by, um, selectively selecting the new ruler of the country, say maybe a general that's willing to put it all on the line. Then something strange happens, like US suddenly causes (pays for) a million tons of rice to show up in ROK for shipment north.
A bargain. Oh, southern Koreans intermingle with north Koreans...interesting conversations happen...

That presidents from Nixon on found themselves paralyzed by the problem of Korea speaks to their assessment of it's difficulty. Trump's outburst may be emotionally satisfying and feel like "cutting the Gordian Knot", but it could lead to a much worse situation.

Or, kicking the can down the road just ended. Kim will either shut up, fire off some non-nuke missiles to Guam (I'm betting that doesn't happen) or get pneumonia.

As I (and Douglas Adams) say...don't panic.

It ain't about nukes. Kim got nukes. It's about engineering. Got to make them small enough to fit on an ICBM, if you want to threaten Uncle. But, in the mean time...

FTA " Under the accord, North Korea would agree to allow full and continuous inspections of its existing nuclear sites, freeze and then later take apart some of its most important nuclear plants and ultimately ship out of the country fuel rods that could be converted into fuel for weapons.
But the agreement also allows North Korea to keep those rods for an unspecified number of years. This provision means that the potential that North Korea could break its agreements and quickly produce nuclear weapons will not disappear until the end of the decade."

In other words..."OMG CLINTON GAVE THEM NUKES!!!!!!!!1121!!!!" is entirely accurate. He let them have the rods they were using for fuel.

Don't you really know anything about nukes?