Is it normal for my fingers to be numb when I am 8 months pregnant?

Numbness. Most pregnant women will not develop numbness of the fingers or hands during pregnancy. A small portion will develop this condition as a result of compression of the nerves in the wrist secondary to carpal tunnel syndrome of pregnancy. This usually resolves after delivery. If it gets worse during the pregnancy, go see your doctor. You might need to be referred to a specialist.
No. This is not normal. You should have your circulation and nerves evaluated.
Not common. Although not common, swelling of the arms can cause pressure on the nerves int he wrist and produce carpal tunnel syndrome, as dr. Holgado said. Wrist splints can help until delivery, then it should go away its own.