What can cause vaginal bleeding a year after a hysterectomy?

See your GYN. In the process of healing, any incision can develop granulation tissue, which is normal collection of blood vessels and connective tissue. Granulation tissue can also form at the top of the vagina in the months after hysterectomy. You should see your gyn to determine the source of the bleeding, and if it is granulation tissue it can be easily treated in the office.
It depends. Not all hysterctomies successfully remove all bleeding. When the cervix is left in place, called a supracervical or subtotal hysterectomy from 2-18% of patients will continue to bleed. There are techniquies that can lower his risk but this is a major cause of the bleeding to which you refer. If in fact the cervix was also removed other causes like infection, trauma, or cancer must be ruled out.
Varies. Yeast, atrophy, infection, granulation tissue, and cancer are some of the possibilities. See your doctor for an exam.