Can I buy an iPhone on eBay after losing mine, and have AT&T put my service on my new phone even though I didn't purchase it from them?
You can buy an iPhone form eBay and AT & T can put their services. You can also choose to buy one from eBay that is from AT & T which will cost you the same amount. Go to http://www.ebay.com/ctg/Apple-iPhone-4-16GB-Black-AT-T-Smartphone-MC318LL-A-/99998176 for details.
Yes. You would have to buy an unlocked phone or one that was used on the AT&T cellular network for it to be compatible.
You can do this. You will have to be sure that the iPhone is an AT&T iPhone though.
Absolutely, just be prepared to pay more, buying an iPhone on without a upgrade/contract renewal is pricy.