One Japanese politician purposely leaked that they too have some nuclear fuel rods unaccounted for AND suggest that they can assemble a shake-and-bake nuclear device in very short notice. Well, Kim can take this as a bluff. You never know before you try, just like Israel who never admitted they have nuclear weapon.
We don't know. Nor do we know if the North Koreans really are. That's what makes this so interesting. The Chinese really do have a good deal at stake in maintaining the status quo, for a change, and the North Koreans are trying their best to upset it. In the absence of a potential Japanese nuclear program I think the Chinese would be more than happy to let NK continue to be a pain in the U.S.'s collective butt.
What we do know the Japanese are doing is (1) pursuing an active missile defense program, and (2) openly discussing modifying several key provisions of their constitution, the ones prohibiting them from developing offensive armaments. That alone will cause some midnight oil to burn in Beijing. I think - it's just IMHO - I think the Japanese would certainly pursue an active nuclear program should the North Koreans perform a successful test, and I think they'd be silly to wait until that actually happened. There's too much at stake, and time is precious. And that's what the Chinese are thinking about.