I ask because Zod came due to the scout ship sending a distress signal. Zod was pretty far away...so how long did it take Zod to get to earth, or how long did it take for the distress signal to travel through space?

I'm not sure, but didn't Perry White gave Lois Lane 2 weeks without work and pay for giving her article to the hacker guy, though when Zod sent out his message, she was at the Daily Planet trying to print something.

It’s even gets better – in the beginning of movie, when Lara found acceptable planet for Kal-El, computer modeled image of typical human. It looked to me like frigging caveman or something.

This is from official adaptation of the movie.

She had lost her ability to track her son’s starcraft

once its phantom drives had activated. The drives warped

both space and time, taking the tiny ship beyond the

scope of her instruments. By the time it reached its destination

on the other side of the galaxy, millennia would

have passed from her perspective.

That ice age she had glimpsed would be ancient history

long before Kal-El arrived at his new home. And

those primitive savages should have progressed

considerably.

Add series of jumps through space when Zod and his followers were searching for Codex. Timeline in movie is total mess.