USA surely wont be afraid.. But I don't think they've would want a war with a nuclear armed state.. Don't forget China might have Russia on their side in an event of a war with USA. It will be their best opportunity to bring down USA.
So in my opinion, I don't think USA would ever risk a full scale war with China.
The shooting war I am referring to was IF and ONLY IF Chinese CG would patrol DiaoYuTai on a regular basis. How would Japan react?
No. China will not have Russia on their side, no one can have Russia on their side, look at it this way, during Korean War, when both China and North Korea are Russia's allies, the Russian did not really participate. In Vietnam War and subsequent Sino-Vietnam war, the Russian did not really participate too, other than provide weapons (for a price) to their ally.
In the event of a war (if there is one) of China with US and her ally, you can be sure that China will be alone in this one.
Anyway, you are correct to say that US would not want to go into an all out war with a nuclear armed state. Because desperate people would do desperate thing... so it is up to your imagination what China will do when she was on the verge of being defeated.
As to the scenario of Chinese CG patrolling the Diaoyutai water on regular basis, I believe the Japanese will not really react too much, not that they are afraid or what, they might make a few compliants, show some angry faces and the such, but will not really do anything, except, maybe spray water at intruding fishermen or CG.
Things will go haywire only if either side land on Diaoyutai and started building some permanent structures.