[LeoDox]

Mars has an iron core; it's just not molten which prevents it from being ferromagnetic.

I have three questions:

1. Is it merely a question of mass? That is, if Mars were larger would the increased gravity increase pressure at the core and keep it molten?

2. If it IS merely a question of mass, is there any way to add mass to Mars which doesn't disturb its orbit? Because if you could, then you simultaneously solve both the problem of low gravity AND lack of magnetosphere, which together solve the problem of maintaining atmosphere. Basically the whole planet becomes extremely Earth-like

3. If increased mass wouldn't necessarily wreck its orbit, could something be done to "steer" asteroids from the Main Belt into collision courses with Mars?

I really don't know anything about orbital mechanics so maybe there's an obvious flaw in this (aside from the energy required to reroute that many asteroids).

[nine_k]

The amount of energy required to lower the orbits of enough asteroids (e.g. 20% of Mars total mass) is probably enough to melt a significant portion of Mars. Unfortunately, collisions would mostly heat up the surface, not the core. Even if you could precisely deorbit enough asteroids to hit Mars, the results of the bombardment would probably take a long time to settle.

Planetary-scale engineering is not only hard, it's inevitably slow.

I think cleaning up the atmosphere of Venus by spreading CO2-eating anaerobic air-suspended algae is more realistic, and the results would likely be nicer.

[Symmetry]

It's not pressure but heat from mostly radioactive decay and also tidal stresses from the Moon that allow the Earth's core to be liquid. More mass allows for more insulation and more decaying Uranium, Thorium, etc so tends to lead to higher internal temperatures.