China in the middle?

Hardly.

One thing I don't understand when it comes to North Korea - why does anyone in the U.S. want China to mediate?

If they're successful in ending the North Korean-manufactured "crisis", they've strengthened their role as a growing superpower region. And if they're not successful, they've prolonged a crisis that serves their other interests.

From China's perspective, conflict between the two Koreas has been one more stick to use as leverage when dealing with the U.S.: "We may be waging currency war against you, but if you retaliate, North Korea may just blow up Seoul."

The truth is, China doesn't have as much influence over North Korea as seems to be commonly assumed. It can't stop North Korea from attacking the south, let alone change the country's paranoid narcissistic nationalism.

The real solution is for South Korea to prove that North Korea is a paper tiger. The problem is that South Korea is not prepared for an actual war, let alone one where nuclear weapons might be used.

If North Korea continues to back itself a corner, real conflict is inevitable. the miracle is that it hasn't happened yet.