Does Boost work together with Google analytics? This may be a stupid question, but can the Google Analytic module still track users and count page visits etc. if I use Boost module to speed my site up? 

Is there anything I should be aware of? Are there any settings I must do in robots.txt for example? (Other than the line Disallow: /boost_stats.php which should be entered according to the instructions).
I am not a Boost expert, but I know Google Analytics. Google Analytics is client-side JavaScript, so as long as your pages render the Analytics code along with everything else in the HTML, you should be fine. Boost should have nothing to do with it.