Is the moon drifting away from earth?

Yes. by a few cm every year. The moons gravity effect on the earth is slowing the earths rotation, which in turn is weakining the earths magnetic field, which is keeping the moon in orbit. Eventually if nothing crashes into the earth, and if the sun doesnt explode, then the moon will escape the magnetic field of the earth and find its own orbit around the sun, however this orbit would not be as circular as the earths, it would most likely move much closer to the sun at some point in its orbit and would probably fall into it.