Are jaw spasms normal after having a tooth extracted?

Possible, not normal. When elevating a tooth out of its socket, the surgeon will place intense pressure on the jaw which can sometimes lead to post-operative jaw muscle ache and even spasm. This is avoided by adequately and comfortably supporting the patient's jaw when this pressure is applied.
Sometimes. Prolonged tetanic spasms of the jaw muscles following extraction is known as trismus and is caused by inflamation and edema in the muscles of mastication. During extrractions these muscles often get overly stimulated from wide and /or prolonged opening during surgery. Normally the spasms will resolve spontaneously. You can seek comfort by applying warm compresses to the area.
Maybe. You probably have TMJ syndrome and sometimes it gets triggered by opening you mouth wide for sometime during extractions.
Sometimes. Sometimes. More common with wisdom teeth extraction. Can also occur from local anesthesia injections to lower jaw teeth. In any event, if your symptoms last longer than a week, go back and see your dentist.