1. Do I understand this greeting correctly to mean "The Peace of God [Allah] be upon you"?

2. Is it, as I have spelled it, the correct american english spelling?

3a. I can bet that there are some Muslims that may think that I (as a Christian) am not being sincere if I greet them in this way. I have many close friends who are Muslims who say that most Muslims would accept the greeting as "fully" as they would accept it coming from another Muslim. Do you believe this is true?

3b. Are there instances where you would recommend that I (as one who is not Muslim) should not use this greeting to a Muslim?

I know I've asked a lot... please bear with me :)