It does happen to a lot of riders, maybe most at one time or another, but I wouldn't call it "normal." Nerve damage has a tendency to become cumulative, because it heals so slowly. So you don't want to let it progress to the point where you're having trouble off the bike, or where you can't ride comfortably or safely.
Fit-wise, if you haven't already had your bike fit to you, that might be in order. A change in position of your handlebars or saddle, or a different stem, saddle or handlebars, could take some of the weight off your hands. When you say your elbow felt stiff, are your elbows locked when you ride? Try to keep them slightly bent. That will take the stress off your elbow joints and let your muscles absorb a lot of the vibration. Your physical program should include core strengthening as well as neck and shoulder stretches. You might also try different gloves and/or bar tape.
Enjoy your first century ride!
Speed comes from what you put behind you. - Judi Ketteler