1. If you don't want to pay for bandwidth, put a lobby server on the amazon cloud (or somewhere else that happens to be reachable), and let players run their own (perhaps even -- dedicated) servers that will register with your amazon cloud lobby. This will also let you easily hot-swap servers if you need to move the actual game server elsewhere.
2. If you shut down the actual game server, then yes, all games will be canceled of course. However if you follow my tip from #1, then you can have many servers that won't be on Amazon.
3. Completely random open channel.