| MadSci Network: Astronomy |
You're very perceptive in realizing the key difficulty in terraforming the Moon to give it an earthlike atmosphere: its gravity is too low to contain a large atmosphere for a long period.
All planets with an atmosphere lose gas due to a process called thermal escape. Molecules in a gas have a random distribution of velocities. There will always be some molecules in the atmosphere which have velocities higher than the escape velocity of the planet. This means that if they start out moving away from the planet with that speed, gravity will never be strong enough to bring them back. In the very thin upper reaches of the atmosphere (the "exosphere"), the mean free path (the distance air molecules travel before hitting another molecule) is large enough for the high-speed molecules to escape without hitting anything. Once they're gone, sunlight warms the atmosphere to produce more high-speed molecules, which continue to fly away, eventually bleeding the entire atmosphere away to nothing.
For the Earth, gravity is strong enough that the time required to do this is many billions of years (longer than the life of the Earth), and vulcanism and other processes help to replenish the gas supply For the Moon, it's much shorter: perhaps tens of millions of years. This is why the Moon has no atmosphere today.
So any attempt to give the Moon an atmosphere is going to be a temporary one. However, ten million years is a long enough time that most humans aren't going to worry about it.
Where can we get the atmosphere from? One possibility is to heat up lunar rocks to the point where they release the oxygen found in them. This requires absolutely vast amounts of energy. The energy needed might best be supplied by underground nuclear explosions. However, you'd need 10^10 (ten billion) one-megaton nuclear weapons to do this, at a cost of tens of thousands of times the current world gross national product. However, it might be possible to make it much cheaper. If the explosions happen near the surface, you'd end up pulping the entire surface of the Moon to a depth of 100 meters.
Another possibility is to use the gases frozen in comets and the icy satellites of the outer solar system ("iceteroids"). Clever schemes for modifying their orbits by nudging them with nuclear weapons and using the gravitational "slingshot" effect have been proposed: one could in theory arrange to have these bodies strike the Moon, instantly vaporizing the frozen gases and providing the Moon with an atmosphere.
This tactic could also help with the second problem you mentioned: the slowness of the Moon's rotation. By striking the Moon a glancing blow with the incoming iceteroids, one could cause the moon to spin faster.
However, once again a lot of effort and material is needed (10^18 kg of gases are required). A single icy satellite 500 km across, such as Saturn's satellite Enceladus, would supply enough atmospheric gas and give the Moon a 10-day rotation rate. There are advantages to cutting it into chunks first. But the entire solar system has fewer than a dozen bodies of this size: there are ethical questions to answer before we destroy a unique heavenly body to temporarily modify the Moon to our liking. If we chose to deflect comets into the Moon's path instead, we'd need to use up every new comet entering the inner solar system for 10,000 to 100,000 years. An alternative is to go out into the Oort cloud (where the comets live) and deflect their orbits into the inner solar system.
As you can see, it's a tough problem, but I hope this has given you some ideas. Most of the information in this answer came from Martyn Fogg's book Terraforming: Engineering Planetary Environments (ISBN 1-56091-609-5: I got my copy from Amazon Books). This is so far the only technical book on terraforming in print, and Fogg has done a remarkable job of describing the remarkable ideas of people interested in the field. I highly recommend it.
Try the links in the MadSci Library for more information on Astronomy.