If the moon is losing energy dragging the oceans around, why is it moving away from earth instead of falling like any other satelite would? If a satellite loses energy it starts to circle lower and finally hits the atmosphere. The moon is moving like an inch a year away from the earth even though it is losing energy pulling the oceans around.
No. The energy budget of the Moon is actually increasing. The Earth's spin is slowing down, and that energy gets transferred to the Moon.

Why is the Moon receding from the Earth due to tides? Is this typical for other moons?

Whatever else may be happening (like the losses you mention), this transfer from Earth's spin to Moon's orbital energy is the main process responsible for raising the Moon's orbit.