Does moon have gas

No it has no gas. It is fairly dead.

Moon - negligible amount cuz of low gravity and proximity to the Sun.

Hot gas molecules move faster and on the Moon gas velocities for those temperatures exceed escape velocity of Moon (i.e.. too low gravity) and hence have left it.

But if the moon was farther away from the Sun and not too far that its temps fall to near zero (-273.15*C where all gases liquify) it could have a thin atmosphere made of the right kind of gas to suit the temp.