Let says I want to send 1 XMR to Alice, and I want to prove to EVERYONE that I sent that 1 XMR to Alice without giving them a view-key or anything. Is this possible, and where could someone view the transaction?
The view key would not allow you to prove you made that transaction. To prove that you sent those monero to Alice you'd need to provide the Tx Private Key, the recipient's address and the transaction hash to the people you want to prove that the payment was made.
You have to setup your wallet to save the Tx Private Keys using a switch that I can't really remember now.
There is an online tool run by one of the coreteam members (luigi1111) that lets you check that: XMR Tests. (Since the moneroblocks.info lazy maintainer is yet to add SSL to the API, you can save the page and run it from your own computer)