In times of emotional stress , certain hormones cause the blood vessels in the hands to get narrow. With less blood and more active sweat glands, your hands may be cold and sweaty at the same time. But sweaty arm pits is normal and like the cold, clammy hands, it can get to be a bigger problem if you're stressed. It's caused by the interaction of sweat with the bacteria that normally hangs out on your skin. Regular washing with soap and water helps eliminate bacteria on the skin.
Antiperspirants reduce sweating while also masking natural body odors with perfume.
There really isn't any. Sometimes teens who sweat excessively find that by the time they reach their twenties they don't sweat as much. Maybe their bodies have gotten more in gear. Maybe as we get older, we get better at dealing with stress. If you think you've got it, discuss it with your doctor.