Can we park our car there all day if we want to view both day and evening? Or do we have to move it between 4 and 5pm when they are closed?

You can leave your car in the parking lot. You will have to exit the actual park and re-enter for zoo lights, but your car can stay in the parking lot.

We only went for the day but they had ample parking. As for if you can park in between the regular hours and zoolights hours you could contact the form the info on their web site list on Google maps.

To the best of my knowledge, if you want to visit the zoo and then stay for Zoo Lights (or some evening event like that) you can just leave your car in the zoo parking. Otherwise, I believe the rest of the park is closed after 4 or so.