NO, every object falls at the same speed. Paper and feathers fall slowly because the air has to slide to the side and back really fast for them to fall. Since the moon is close to the Earth, the gravity has put mile high bulges in it. The moon gives the Earth high and low tide. The Sun effects the weather, for an example it gives most places four seasons.
Astronauts are taller in space because on earth they're bones are pushed closer together by gravity.