A. The idea of keeping the Lulav until Passover is to burn it together with the Chametz, this way we continue its use in another Mitzvah, acting as fuel for the fire of burning the Chametz. This is a custom and not a law, it is simply to keep the Mitzvot energy flowing… Recycling Mitzvot in another form! Personally I try to do this each year and fail since the Lulav becomes moldy long before Passover, or the kids hurt each other with it, so it isn’t practical for us. Some people make Etrog jelly or jam, and eat that on Shabbat, some use it as Besamim (pleasant smelling spices) for Havdalah, especially if you stick cloves all over it. We cut up the Etrog and throw it into a punch or lemonade mix and enjoy it on Simchat Torah. But these are customs are not the law. You do not have to keep the Lulav and Etrog.