When you start the menopause do you stop having periods?

Yes. By definition, menopause is the cessation of periods for one year. But if you are younger than 40 and don't have a period for a long time, this should be evaluated by your doc to be sure it isn't form another treatable cause. Further even women in menopause should continue annual gyn visits to stay healthy.
Yes. In menopause the ovaries are no longer producing both estrogen (estradiol) and progesterone, which are potent female hormones. Every cell in a woman's body has estrogen and Progesterone receptors, when there isn't estrogen and Progesterone in the uterus, the uterine lining doesn't grow and so a woman's period stops. You can replace your hormones and restart your periods by starting cyclic bhrt.