You can use a new ball for every hole you play. You can not change balls during the hole, unless the ball is damaged. It makes, sense, else everyone would use a different ball for every circumstance during the hole.
You have to play the same ball you hit off the tee until you get it on the green. Then your ball may be picked up and replaced if wanted with another ball.
Yes, you can replace your golf ball between holes if you choose. Between strokes on the same hole, however, you must continue to use the same ball. You are allowed to lift and clean your ball once you are on the green.
Yes. You can play a different golf ball on every hole, but you are supposed to use the same ball for the entire hole. Changing the ball on the green is against the rules.