When I get toothache sometimes it goes numb, is this normal?

Both. Toothaches and being numb without an injection of local anesthesia is not normal. That's two good reasons to see your dentist and have the problem(s) addressed. Infections can cause inflammation to the nerve and subsequent numbness. Don't take a chance of nerve damage and bigger problems. Set up an appointment today.
Call dentist ASAP. You may have an infection that is putting pressure on the nerves in your jawbone, causing the numbness. Prolonged infections like this can cause permanent damage to the tissues. Don't wait for a major emergency.. Call at once.
Sometimes. When an infection gets close to the nerv it may cause that numbness. Visit your dentist asap.
No. No. There is a serious problem with the tooth. See your dentist for evaluation/treatment.