If it stops raining, will the puddles and ground remain wet for a while or will they dry out immediately?

Yes, we've recently just changed that so it does do what you would hope it would do. So it keeps track of the average amount of water in the ground and it evaporates over time using a physically plausible model, which we tweak to be a cross between whether you want it realistic or what feels good for the gameplay based on the scale of our planets and the wind speed and stuff. Yeah, it will stay wet for some period of time after the rain has passed. So we're all good there.