2) Analytics will give you a % Bounce Rate for pages, keywords etc. You may not be able to easily distinguish between a click on an internal link or a click on an Ad, but you should be able to pick out those pages or keywords that result in an immediate "back" or "close".
3) Analytics provides an enormous amount of data that I find fascinating - if it's useful as well, that's a bonus. I believe that all you have to lose is your time setting it up, and your time looking at the data - although some others here have suggested that Google uses the data for more sinister purposes.