I wonder if one built a large superconducting magnet on the poles of the moon, whether it would enable protection from the solar wind and potentially enable an atmosphere that could support some kinds of life.

Assuming atmospheric pressure is directly proportional to gravity and height, and the gravity of the moon is 1/6 of earth; With napkin math, this puts the potential atmospheric pressure at 1/36th of earth, or 0.41 psi. At this pressure, water is liquid between 32F and 71F. It's likely the moon is too close to the sun to sustain this low of an average temperature, but I don't know the principals behind computing that value.

If the atmosphere contained enough ozone, it might filter out enough UVC and X-rays. Under these conditions, and if somehow we could find a source of CO2, NH3 and O2, the moon could easily support plant life and begin building enough soil to feed any population.