If the moon contains an atmosphere and oxygen, would life be possible?

Answer

If the Moon or Mars had an atmosphere like ours, people should indeed be able to (survive) live there.

An important condition for comfortable living is that there is enough water, and that would be a problem on the Moon today, and to a lesser extent on Mars. But that problem wouldn’t have existed if the Moon had had an atmosphere from the beginning, because it is the lack of atmosphere that makes it very difficult for the Moon to keep up with water. However, small amounts of water are present in the lunar crust.

Perhaps the most annoying of both heavenly bodies would be that you weigh less than with us. This would lead to bone loss (your bones become less strong). We don’t really know what long-term effects this has on humans. We do know that it will certainly cause problems if you come back to Earth.