Not more than others. The recommended daily allowance is the same as people without thyroid disease.
Not specifically. Supplementing with calcium and vitamin d is recommended for all women to prevent osteoporosis. In patients with hyperthyroidism, supplementation becomes even more important because there may be increased bone turnover. For hypothyroidism the recommendations are no different than for the average woman.
Depends. If you are menopausal, you should add extra calcium, but be sure you don't take the two pills around the same time. Best to take the calcium after lunch or dinner. If you are male, a small amount of calcium may be in order. Also, take some vitamin d. Please discuss this with your doctor to get specific advise.
No. No need unless I am missing some information.