Sure, so we'd better get started.

The assumption is that we will somehow "terraform" Mars so that it will be earthlike before Earth is destroyed.

why would martian life survive the destruction of earth from extraplanetary impact, which would affect martian orbit?

Mars is only the spearhead for further stellar and maybe even interstellar colonization, after all, we gotta start somewhere don't we? Once we manage to do Mars, by gaining knowledge, developing technologies and maybe even discovering new resources, we can hedge humanities survival further by applying this experience to colonizing other places in space.

How would that affect Mars's orbit? The remains of the Earth will keep on orbiting the Sun.

Indeed. We'd have to start somewhere, though.