1. Standard rooms must be available to use the N&F award. You can use the online reservation tool to check and see if standard award rooms are available. If so, then the agents should be able to make your award reservation. If not, then they won't be able to.
2. It is possible that there was availability during your first call, but not by the time you made your later calls. I guess it is also possible the first agent made a mistake and the others are correct as well. As stated in #1, you can use the online reservation tool to see if there is any standard room availability for your timeframe.
3. The miles will be deposited into your airline program of choice and at that point, any use of them is dependent upon the rules of that program. SPG has no control or knowledge of how/when/where you would spend those miles. (Though I'm sure they would like for you to use a Starwood hotel where ever your travels take you.

)
4. Yes, that is a protection to make sure no one else can use your account through a phone agent. Your phone password does not have to be, and probably shouldn't be, the same as your online password.