No. I don't believe it has anything to do with the actual Mafia Wars application. I have had friends send me specific items and I have never seen them in my inventory. It just posts to my Facebook...
Yes. You can buy Reward Points but the game is free and you don't really need Reward Points to play the game.
Yes
Asian Museum Break-in ..in NY at Soldier tier
There is no free mafia suit. You can buy a mafia costume from other players.