Does the moon have swing

So it goes down with the distance you are from the center of the planet (r) and it is the speed you need to be after all launch forces have stopped eg jumping or being shot out of a cannon. It does not apply to weather balloons or rockets who make it to orbit.

There will be a point where you'd be able to jump or swing into space but it would be a long way from the surface of the moon.
One thing that may be problematic is the chain or rope tension. If you ever go really high on a swing (near horizontal) you can easily pull in on the ropes and cause you to move towards the pivot. On earth the gravity is so strong it keeps the system in tension. On the moon it will be much easier to pull the ropes together and move yourself towards the pivot.
Yes, a swing would work on the surface of the Moon. But because the acceleration due to gravity is lower on the surface of the Moon, the motion of the swing would be slower (all else being equal). Since to the first order the period of a pendulum is inversely proportional to the square root of the acceleration due to gravity and the gravitational acceleration on the surface of the Moon is 16.6% that on the Earth, the period of the swinging motion of a given swing would be ~2.5 times longer on the Moon than on the Earth.