We have a 600gallon / hr pump (so it says on the box), and a 1800 gallons pool. So I would go with 3 hours at least of running the pump a day.
Is that correct?
Should it be run during the day and / or night?
If it were mine, I'd start with more than I think I need, and then gradually reduce it. There's every chance you're fine right where you are, but you'll only know with a bit of experience. Basically, if the water is as clean as you like it, you're pumping enough, so you can try reducing it a bit and see if it's still just as clean. If it's getting lots of use, that stirs the water up, so then it's just about the filtering time.
Day or night is not very important, but certainly run it for a while whenever you add any chemicals. I like daytime myself.