In my opinion, would not allow any sort of war against North Korea without their direct involvement. So, any hope of a 2 week victory is naive at best. The reason North Korea even exists is because of China.
North Korea is going to do what they always do...grandstand to get attention. They seem to do it every few years or so, but nothing major happens.
Japan has a right to shoot down any incoming missile that crosses into its air space. They can choose to retaliate if they want, but I don't think they have any desire to go into another war unless there was no other option.
I don't like that the United States is over there, but we have been for many year. Since we now pretty much have to stay for an economic partnership with South Korea...what are our options? I would say try and maintain peace as best as possible.