Should I do something about these cracks in the basement wall?
It looks like moisture under the skim coat has caused it to separate. To repair chip off the loose material and add a new skim coat and repaint. If you have a drainage problem this may continue to happen over time as the moisture working its way through the wall is the problem. Make sure all gutters drain away from the foundation. If you have a sump pump try to keep the water level low so the water has a tougher time making it in.