Usually local. Thyroid biopsy is usually done with a small needle under ultrasound guidance under local anesthesia. Unless you have anxiety disorder, sedation is usually unnecessary. It only takes a few minutes and complication is rare.
Needle biopsy? If this procedure is done as a simple needle biopsy then it can be done with conscious sedation. If this is going to be an open surgical resection I believe the best treatment would be a general anesthetic. Please discuss this with your provider before the operation.
Yes. A biopsy of the thyroid could easily be done with IV sedation.
Not used. A thyroid biopsy is a very simple procedure, performed with fine needles. It is very well tolerated if performed by a skilled professional. Only local anesthesia is required. General anesthesia is sometimes used for very young children.