Can uterine prolapse cause bleeding?

It is uncommon for prolapse to cause vaginal bleeding.

Do not assume that vaginal bleeding after menopause is due to prolapse. It is not normal and should be evaluated. 

Can uterine prolapse cause heavy periods?

In general, a uterine prolapse is not associated with heavy periods. There are many gynecologic conditions which can be associated with heavy periods, so a visit to the gynecologist is warranted.