Are my heavy periods contributing to my low iron?

Quite possibly. Low iron, which is associated with anemia, is commonly caused by chronic blood loss. Heavy menstrual bleeding and/or prolonged bleeding can lead to iron deficiency and anemia. Fatigue and exercise intolerance are common symptoms.
Yes. If nothing else, heavy periods aren't making your iron levels any better. This is a major cause of anemia for women of child bearing age.
Yes most likely. There are lots of treatment options you can discuss with your doctor. Lysteda is a nonhormone medication designed for heavy periods. Some benefit from birth control pills, patch or nuvaring. Mirena (levonorgestrel) iud can stop your period in some cases. Consider an endometrial ablation such as genesys hta if you are done having children. These can be done in the safely and comfortably in the office.
Yes you have choices. Besides taking iron, abnormal periods need evaluation; sonogram, lab tests. Non-surgical options include: birth control pills. Lysteda (non-hormonal rx taken during period), Mirena (levonorgestrel) iud. Minimally invasive options: endometrial ablation (in-office), hysteroscopy polyp removal or fibroid resection; and only if these treatments fail then consider hysterectomy - vaginal or laparoscopic if possible.