While the overwhelming majority of thyroid cancer cases are not hereditary, certain subtypes (especially Medullary Thyroid carcinoma) can occur as a part of familil cancer syndrome ( Multiple Endocrine Neoplasia Type 2). Infrequently, other forms of thyroid cancer ( Papillary and Follicular) can be seen in multiple family members either due to common exposure to enrviromenal factors such as radiation or less likely due to underlying genetic factors that can put individuals at risk for thyroid cancer (Cowden Syndrome for example).
While there is no particular diet recommended to combat thyroid cancer, your physician might ask you to be on low iodine diet for short period in preparation for tests such as whole body iodine scans and treatment.
There is no data to support the use of over-the-counter supplements to treat thyroid cancer, and it is highly recommended to consult with your treating team before using any supplement for other reasons, as some over-the-counter preparations can interfere with thyroid hormone therapy.