If a person lived on the moon would they live longer since their heart muscles wouldn’t have to work as hard to pump blood?
On average, probably yes. Besides the strain on the heart, gravity also causes broken bones, which can lead to death sometimes.
It wouldn’t affect maximum lifespan though, since that is determined by various genetic factors. If you weren’t destined to die from a a heart attack or a broken bone, living on the moon wouldn’t make you live any longer.
This is assuming that you live in a moon colony far under the surface, and therefore aren’t getting an increased radiation dose, which would certainly shorten your life.
I don’t think this is correct. It is known that astronauts and cosmonauts who have spent long stretches of time (several months) in microgravity have some (reversible) health problems, including bone loss and muscle atrophy. Additionally, the Moon lacks a thick atmosphere to block out the more damaging high-energy cosmic rays that bombard every body in the solar system. Read more about the health effects of spaceflight and low gravity here.
Overall, I think our lifespan would be significantly less on the Moon than it is on Earth. Remember, our bodies evolved to deal with gravity and its effects. And radiation exposure is never a good thing if you want to live long.