Can i track source of purchase? For example, i want to track how much purchase has been from official web-site and how much purchase has been from web-site of your partners. Can i do this with apple app store?

Not sure about purchases, but I know Flurry is a great analytic tool. Check it out!

You can also set up bit.ly urls to track clicks, not sure about purchases though

As far as I know there is no way to find out from where user comes to iTunes and bought the app. There are some workarounds that are used by pay-per-install systems but this is usually to track is user purchased app after clicking on ad somewhere in other app.