according to your first photo that's exactly how it should be setup. that's not exactly a floyd rose but an edge or lo edge pro by ibanez which is based on the floyd rose patent. it's a floating bridge so the bottom of the tremelo should be flush with the body. this allows you to both depress and pull up on the bar.
if you change gauge strings you will have to adjust the springs. you will also have to adjust the truss rod to adjust the relief in the neck. if you're not experienced in doing this i'd take it to a shop and ask 'em for a $10 tutorial.