Here is a huge link that can help you understand what you are asking.
http://thyroid.about.com/od/thyroidbasicsthyroid101/u/coping.htm
It is a large article and should cover many questions you have.
Thyroid hormones can have a direct effect on estrogen. There's a lot of controversy about whether or not women with hypothyroidism have longer and heavier periods. (Many say that they do.) What you will here on this forum is a lot of personal experiences. I know for me my periods were lighter and shorter on high doses of thyroid replacement meds and so were my sisters and daughter.