1) They’re on top of the world since they had a baby.
=> They are extremely happy about it.
=> IDIOM: to be on top of the world.
2) I think the world of my parents.
=> I value and respect them.
=> IDIOM: to think the world of someone.
3) Nothing much. Just sitting here watching the world go by.
=> I am doing almost nothing, I’m just sitting around.
=> IDIOM: to watch the world go by.
4) He had the whole world at his feet by the time he was 30.
=> He had become extremely successful, popular and admired.
=> IDIOM: to have the world at your feet.
5) Congratulations on your new job. You’re really moving up in the world.
=> You are becoming more and more successful.
=> IDIOM: to move up in the world.