Hello Pelin, "I was never a child." and "Morality requires such behavior." are correct as long as you state what kind of behavior you mean in the same paragraph or near this sentence so readers know what behavior you are referring to here. Here are my edits to the other two sentences plus a couple of alternatives:
I didn't have a childhood.
I never had a childhood.
Morality requires behavior like this.
Morality requires us/people to behave like this.
This is how morality requires us to behave.
Hope that helps.