In certain cases. Many thyroid nodules need to be surgically removed, while others will never require surgery. Each case is individualized and there are many gray areas. It is really difficult to give a meaningful response to that question in the absence of a history and physical examination.
No. Only cancerous nodules, or those for which cancer can't be ruled out, need to be removed. Since 90-95% of thyroid nodules are benign, thyroid nodules that are very small, have low risk features on ultrasound, or have been shown to be benign with an fna, or biopsy, do not require any treatment. They should be re-checked with repeat exams or ultrasound to make sure they are not growing.
Size? Nodules with suspicious features over 1 cm should be biopsied under ultrasound guidance to determine if benign or suspicious. There are molecular tests to help avoid surgery as well.