Does my mom's brothers and their father's brothers and sisters and their children all dying from different cancers increase my risk?

Yes. When family members come down with different types of malignancies there might be a hereditary factor ie the BRACA gene for breast or a mutated APC gene for colon cancer that might be involved. Otherwise there is the question of whether there is a carcinogen present that family members may be exposed to. When MMTV virus causes breast Ca, husbands have a high incidence of prostate Ca from MMTV.