Does adsense ads track where the traffic to your site is coming from, therefore this is a way Google finds out about your traffic? For example, does Google know if the traffic come from Adwords or orther ppc network (yahoo, kontera etc...) or some other traffic providers?
Yes, they track and hence traffic from dody sources is against TOS. There is no point in having that as being against TOS unless they looked at it or enforced it.
Will Google know where user come from if we place adsense not on index page but all traffic will go only to index page (and from index page will go to another pages which have adsense) ?
ya Google do everything. Even google do some thing which we can not imagine. If your IP address is dynamic and if you make fraud click then also google comes to know.
Google tracks all traffic and traffic sources from what i know, they want to try and limit the amount of false impressions and clicks.
I think it's a little difficult if you don't have any Google codes in your site, if isn't I think no.