I wonder if it is possible to choose particular sites on which I want to have my ads displyed? Any filters? And is this service free (if it even exists)? Also, is it possible to choose to have my ads not displayed on any website, but only on Google, when someone searches for my keywords? I think this would be the best traffic for my site.
yes, see the google ad at the top of this forum? under it, it will say something like "advertise here". Thats how you put your ads on specific sites, you have to configure it in your account campaign. And yes, if you look in your account settings, you can have you ads set to only show on google itself.