Is there any way for a site owner to control only what type of Adsense ads on site? I mean that the adsesne content may even not related to the site content? Is that through a "static page "effect on the website?
not directly... You can use Section Targeting to help influence what types of ads appear, you can use the competitive ad filter to prevent certain ads from showing, and you can specify Image ads only, text ads only, or both.. That's about it..
no you can have adsense display ads about health if your page is about something else. If you can do it (like keyword stuffing) then you are in adsense Terms Of Service violation.