How far will it go?
We have no idea. This guy is new to the whole Running North Korea thing, and we just have no clue what to think about him.
Maybe he's serious about intending to attack the U.S. Maybe he's just saber-rattling, the way the North has for centuries, but doing it louder.
We have no idea who this man is, whether he really intends to attack the U.S. or the South, and whether he has the ability to.
Are we taking it serious enough?
That's the big problem. Right now, we don't know, because we have no idea how seriously we're supposed to be taking it.
What should the U.S. do and/or how will the rest of the world respond?
I think the best thing we can do right now is have people ready to go into North Korea, all ready in South Korea. But not go in or make any attack yet. Officially treat it as 'We think they're bluffing,' but be ready to go at a moment's notice.
If we go in, and they're not bluffing, hundreds (or thousands, or more) of Americans and Koreans will die.
If we go in and they are bluffing, hundreds (or thousands, or more) of Americans and Koreans will die.
If we wait for them to do something first, and they are not bluffing, hundreds (or thousands, or more) of Americans and Koreans will die.
If we wait for them to do something first, and they are bluffing, no-one dies.
The best option is to wait. There's casualties if they're not bluffing anyway, and there's casualties if we go in, but if they are bluffing and we go in, people are dying for no reason.
Obviously, up intelligence work in the North as well. If we find enough reason to believe that this is being seriously considered, we have to go on.
As for China.. Who knows, but I think they said at some point they wouldn't support the North if the North launched a strike on Southern soil.