Should I leave the pump running (without pumping in chlorine of course) when doing the overnight free chlorine test? Is there a specific setting I should use? Recirculate perhaps?

Are you trying to kill off an algae bloom? If so, keep the water moving. Imagine you're dissolving the algae, it goes faster if you stir. If the filter is likely to clog up, recirculate. Otherwise, why use all that electricity pumping water and not get any filtration out of it?

The only real criteria is that the pump should have been running for about an hour before you test, so if you get up an hour before the sun and turn on the pump (or have the timer do it) then test an hour later there's no reason to run the pump all night, Unless, like Richard said, you're fighting Algae.