no, you dont need an airstone. It is actualy not recomended at all. You have pleanty of oxygen with the skimmer, though you may need another powerheads depending on the size tank you have.
as far as yoru sand turning brown, it is a very popular occurence in new tanks form a diatom bloom. To help, you can use RO/DI water, have a clean up crew consisting of crabs and hermits and such (most sand sifting creatures are not recomended because they will starve to death and eat a lot of the critters found in live sand), and have good water quality. most likely, once your tank matures, your sand will be clean again.