Don't really think that makes sense. Ad placement, site design, ad relevancy etc... all dominate the reasons of why people click ads. I don't think you're going to get much information about content relevancy out of the CTR as you can't hold those other features constant.
If Google is looking for how useful a page is, they're better off just looking at whether people go back to their search results and click on another site after a short delay.
I think it makes sense in extreme cases. For a 'real' page (e.g. with useful content and ads that are secondary to the main content) CTRs are unlikely to be that high. From experience I would say its hard to get > 10% CTR in such a site.
However, for 'spam pages' (e.g. those that have little information and ad links in primary positions) its common to have much higher CTRs. The prime examples are those sites that present AdSense links in with navigational links so its not clear you are clicking on an ad. CTRs of >50% are not uncommon.
This is correct. If you don't present the exact information someone is looking for but provide links that look like they will, they will click those links.
If Google is looking for how useful a page is, they're better off just looking at whether people go back to their search results and click on another site after a short delay.