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).