I have looked over the T&C and Guidelines or whatever they're called and didn't see an answer to my question, specifically. What I am wondering is can I offer a google search box, and offer a revenue share just for searching through that box? I would not be saying "search and click the ads," just saying, Hey, use this search box for your everyday internet searches and I'll pay you x amount per search. Technically, I figure this would be allowed because I am not encouraging ad clicks, or guaranteeing myself any revenue, but rather saying to use the search box as like, their homepage or whatever. Also, I was wondering if I would be able track what is being searched. Like, on my reports for analytics or adsense if there were 4 searches performed will I see "flu symptoms, chevy cars, how to tie a knot, myspace layouts"... Andddd, my last question, can you put up a new search box for every page you have a search on? That way you can see which search boxes are performing the best (at different locations on the page or whatever). Ok that is all, thanks in advance to anyone that can decipher that mess of mine and (hopefully) provide an answer.
You can use two search box on one page but you can not offer any revenue to your visitor for using the search box.If you do this you will be against the T & C of Adsense and your account will be banned.Try it,if you are not interested in earning money from Adsense.
Prasannas is right. It's really worth spending a few minutes to read the Adsense program policies: https://www.google.com/adsense/support/bin/answer.py?hl=en&answer=48182