Would China join the side of the North again?
No. China has as much to lose with NK going apeshit as does South Korea, Japan, and the United States. They would probably invade from the north to clean up and install a better puppet dictatorship if at all possible.
Would the US pull out of the ME and join the war in Asia?
No. You'd see drawbacks from Afghanistan but the majority of the fighting won't be done by Americans - instead it'll mostly be South Koreans and the Japanese who would certainly be upfront about helping out the South Koreans. Plus the aforementioned Chinese. If it goes on for more than a few weeks the United Nations and NATO will start sending in forces as well.
Would Taiwan see that as an opportunity to formally cede?
No. The Taiwanese government isn't run by fools and idiots.
Would it begin as tactical and then go nuclear?
The North Koreans might use a nuke or two if they really have them, which would probably lead to a limited exchange - probably only against Pyongyang from our side. American leadership, especially within the military will be dead set against using nukes - at least against urban centers - since it won't make any huge sense. Any North Korean attack will be aimed at the Japanese and will probably succeed in killing a few million Japanese. Seoul itself will have been destroyed almost entirely by conventional methods by the second or third day. If anything the Japanese will be the ones very adament for launching retaliatory nuclear attacks on North Korean cities, with American military leaders wanting to using nuclear weapons only for tactical purposes to stem the early North Korean conventional attacks.
What would happen?
At least eight million killed in South Korea. Ten million killed in North Korea. One or two million killed in Japan if the North Koreans have workable nuclear weapons small enough to fit on their rockets, more if they have more than two or three warheads and if the missile shield doesn't actually work (i'm betting it doesn't). At least several hundred thousand Chinese killed and at least tens of thousands of Americans killed. The war is a foregone conclusion as North Korea just goes out with a bang - Pyongyang is probably utterly destroyed, other larger urban centers might be depending on how many Japanese cities are hit by nukes. The Korean Peninsula is probably not reunited and the North is taken over as a Chinese puppet state with closer strings but is generally written off as a functional state for decades. Perhaps the most important thing on the long term is that Japan rearms increasingly and becomes increasing hawkish - something China doesn't want. American involvement is probably overstated.
But i'm just rambling.