Terraforming of Mars

Gravity

The main problem with Mars is it's gravity. The problem is the atmosphere will bleed into space due to low gravity. If we were to melt ice, or in other way add gas (eg. Oxygen) and thus increase the air-pressure, it would bleed into space. One idea of how to increase the gravity is by nudging asteroids from the asteroid-belt, letting them crash onto the surface. This would also have the added effect of adding kinetic energy, in other words, it would melt parts of the surface. Start with metal-rich asteroids, then the water-dense asteroids, finishing with asteroids or even comets with gas-rich deposits.

Oceans and air

All life needs water and air, and it's sufficient to say Mars lacks both. During stage one, the asteroids would plummet towards the surface. And the kinetic energy released by multi-megaton impacts would melt both water locked on Mars and water locked in the asteroids. With sufficient water, the beginning of terraforming Mars will progress from dream to reality. The air could be produced by adding bacteria or algae, splitting Oxygen from water and consuming the hydrogen-atoms for later use.

Problems

Regardless of how one views terraforming, there are problems I have thought about, but couldn't find a solution to solve it. The major problem is to reproduce a similar magnetic field, like the one surrounding Earth. As it is the main protection against cosmic rays, solar flares and other types of radiation. The way Earth produces magnetic field is by a molten core of Iron spinning in the center of Earth. How can this be replicated? Or are colonists supposed to perpetually live underground after colonization? If we could create a spinning molten Iron-core inside Mars producing magnetic fields surrounding the planet, it would make the difference between 'possible to create life on Mars' on one hand, and a short-lived disastrous experiment on the other hand.

The talk about using nuclear weapons to melt the surface isn't a solution, due to increased background radiation. Not to mention wasting nuclear materials necessary for power-plants. Another idea was to add factories producing greenhouse-gases, and it is not a solution either, as the gas would bleed into space.

One far-out idea I got was to use space-mirrors after bombardment of heavy metal-rich asteroids, and before bombardment with water-rich asteroids. The idea was to basically melt large parts of Mars, and use the kinetic energy to create the 'spin' necessary for Mars to create a magnetic field. Basically to start from scratch.

Ok, the ball is in your court, any ideas, thoughts on terraforming Mars?