One: China has, and has always had, close ties with North Korea. Witness the first Korean war.
Two: If the US is nuked, then they will completely obliterate NK. But not only that, if nukes are used, then think about it: All the other western countries will be pissing their pants, and rush to America screaming "You were right! You were right! We're so sorry for your loss! Let us help you get them!". Why? Because they'll be afraid they'll be next.
Three: NK can not do MAD, simply because of the ratio of size in relation to them vs. the US, and the fact that they don't ahve nearly enough nukes (yet) to blow us all to hell.
Four: If there is another Cold War, China would probably win. The US isn't as powerful as it used to be, and the political climate has changed drastically from the 1950s-1980s.