How old does one stop having wet dreams?

Lifelong. If you are a normal, sexually-mature male and do not masturbate or have a partner, you will have wet dreams. One of the cults teaches that these are unhealthy. This is a lie intended to frighten teenagers. I personally know one pastor who left the cult rather than teach this. Being a man is difficult enough without having this frightening and false put into your head.
It varies. Anybody can have a wet dream (nocturnal orgasm). They are more common in men. Unresolved sexual tension or stimulation makes it more likely for you to have a wet dream. More frequent intercourse or masturbation may help. The good news, is they are not harmful.