How quickly can the economy change on a planet? Will it take in-game days, weeks, months?

That's one of the things that you won't really know until you have more time playing with it in-game. Because you have to get a feel for how it looks, whether you detect the difference. And then there's also an algorithm. I would envision you're talking about matters of days, but I don't know if that's going to end up being fun or just too much.