What is the appropriate balance between rest and exercise for a healthy pregnancy?

Moderation. I know some women that continue to run in their third trimester. It is not bad to continue a moderate regimen of walking and light exercise throughout pregnancy. Your obgyn should have plenty of experience in this matter.
Yes. The balance between exercise and rest during pregnancy varies with each individual, and also with each pregnancy. If you are tired on a certain day, then by all means take a nap. When you do exercise use good common sense. Stay hydrated and don't raise your heart rate above 140 beats per minute.