Your son should use a youth model bat. As far as the difference between baseball and softball bats, I'm not real sure. I believe softball bats have a longer barrel width without the taper of a baseball bat.
Batting gloves are strictly optional.
My older son wears 2, my middle son doesn't wear any. I think when a bat has a lether grip, you really don't need a batting glove. BUT, if it makes the player more comfortable, he needs it. Whichever he likes best is ok. Flex or snap action in a mitt sounds like the ease at which it closes around the ball.