It is possible that the phone is just placed on silent, and not completely off. If there is another iPhone in the family, you can try to connect to the Bluetooth of that phone. It will only connect when you are a certain distance, so it should at least narrow down what part of the house it is in. But if it is off or dead battery, then it won't help.
No, military satellites can track with an accuracy to within 6 feet, so I'm sure NSA can at least get you within arm's length of it. ;D