If I have an overactive thyroid, but not graves' disease, should I have radioactive iodine in an amount to kill my thyroid or stop some of hormone?

Goiter orthyroiditis. If not graves, it could be a toxic nodular goiter, or hashitoxicosis, or thyroiditis. Most forms of thyroiditis resolve spontaneously. If the hyperthyroidism has been going on a while, you probably need definitive treatment: surgery or radioactive iodine (rai). Either is acceptable, but requires expertise. Surgery should be from an experienced thyroid surgeon. Talk to your endocrinologist.
Varies. You need to discuss all of this with your endocrinologist in terms of the pros and cons. All have risks and rewards. Don't stop on your own any therapy. If the doc won't give or discuss then get another opinion.

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