1. It shouldn't be any problem to wear a superman costume through security--if anything it will be better for the security people, because you cant hide anything in one of those superman suits :). If I were you I would carry the costume in your bag for the trip - then change into your superman suit in the bathroom in the airport. Just to be comfortable.
2. Believe me, superman is not even weird for New York. A few days ago I saw a guy with full armour on the subway. New York encourages these kinds of freedoms.
3. And yes it is absolutely safe in most of the city.
superman