I frequently experience times when I am extremely sad and sometime later I am elated and feel that I can do anything. Is this something to be worried?

Sounds like you are. Already worried. Why not make an appointment with a psychiatrist who can help you figure this out?
Depends. It depends on the severity of the sadness and elation, the duration, and what else they are associated with. Every body has mood swings to some degree based on things around us to a large extent. Sadness with loss of energy and interest in usual activities or elation with decreased need for sleep are key features of bipolar disorder. Talk to your doctor. He may recommend you see a psychiatrist.