Can I put my adsense code on the chat rooms (that will be displayed on other sites"
Its very risky. One of the main point in Google adsense is you should not be putting adsense on pages which are not reachable something like your test pc on local host. If any of your user does something like this your adsense can get banned.
You can't give your adsense code to other people to have them on their own websites, it can be easily abused and you can't control it once they do abuse your ads.
