The Third TW strait crisis was not to take control of Taiwan, it was to discourage voting... It would be unlikely that another crisis will occur in the near future because China has such an overwhelming advantage over Taiwan, not just militarily but politically, in terms of isolating it from other countries.
whether the mainland "backs down" or not, and against what kind of opfor, depends what their motive is. If it's not very important like the 1996 crisis then they could very well back down against any number of american force.
If it's of utmost importance then you're looking at WWIII.
And I disagree -- talk about the varyag does not revolve around Taiwan at all. All Chinese carrier development is focused for situations beyond taiwan... that's not to say they wont' be useful for such a contingency however.