How long do I have to wait after a nuclear medicine thyroid scan, i-123, to have a fna biopsy and/or thyroid blood tests?

You don't wait. Generaly speaking you do not need to wait at all after having an I 123 thyroid scan to have a biopsy. You usually have the biopsy scheduled after the results of the thyroid scan are interpreted which usually takes a day. The radiation from the I 123 is minimal . .
Radiation... The physical half life of I-123 is approximately 13 hours. To avoid radiating the person doing the biopsy, you could wait until it clears from your system. Other than that, waiting is not necessary. .
Any time. Fna of thyroid can be done any time. Most of the time thyroid hormones are not affected by thyroid scans with i-123. However, in some occasions, depending on the iodine status and the condition of the thyroid there might be a decrease uptake of iodine by thyroid and cause transient hypothyroidism ( wolf-chiakoff phenomenon ).