The starts increase with the amount of posts you have. I don't know the exact number of posts you need to add another star.
The green squares are your Karma level (or points, which you can view in your User CP).
Green squares mean that you are mainly getting positive karma comments from people (the can give karma by clicking the Ying Yang symbol by your post)
Red squares mean that you are mainly getting negative karma.
Black squares mean that the user has disabled his or her karma level.
Some people disabled it cause they think it's silly. Most people keep it on though and that's one good way to see that member is being nice (green squares) or being an assclown (red squares).