1. I think you mean AdSense. You would use AdWords if you wanted to put ads on other peoples websites or in Google search results
2. If someone clicks on an AdSense ad it opens in the same window, so the person practically leaves your store.
3. Jake is right, the earnings from AdWords are relatively low, check out http://webgilde.com/en/how-much-does-adsense-pay/
4. I would not recomment using external ads in your online store, because it not only drives away customers, but takes space. Anyway, to keep an open mind there might be a reason to do so. If you have very specific traffic from people who obviously don’t want your products, but something similar that you don’t offer, e.g. "umbrellas that fit into ones handbag". You might try to put affiliate ads on the landing pages those people are visiting. The art is now to identify those visits :)