Atmospheres come from the rocks and surface, the Moon is continuously generating an atmosphere but it simply gets blown away by the solar winds.
Mars is similar but has residual magnetic fields that preserve some of the emitted atmosphere so you see wind events there.
Atmosphere is simply down to having a global magnetic field, create one for the moon and the atmosphere will stop being swept away and collect just like on earth.
As for water, probably buried under the surface, some as ice. Space has loads of water so it would be shocking if the moon had none.