Did I just read correctly? You called Creepers... "green zombies"? SHAME ON YOU!
Shame on you, sir. Not answering his/her questions. :slap:
Grass doesn't grow, it spreads. If a piece of dirt is near grass and there is a light source (Or the sun) nearby it will spread to that dirt piece. It will continue to spread as long as there is dirt to spread to.
Creepers can be killed by hitting them with a sword and running away before they blow up. They can also be killed by standing inside a room with an outward facing door. You can hit them but they can't hit you.