You set them with the sliders that you have in your first screenshot. Although currently it's broken and the sliders don't work in franchise mode (not sure about the other modes).
The box in the lower right in all your other screenshots is used to set the game to the exact time of day that you want, the purpose being to allow you to control the position of the sun, weather, etc.
Open/Close time is purely cosmetic, it has no other affect on the game, the day/night cycle that occurs as time passes only occurs within the range of what you set as your open hours (effectively, any hours that the zoo isn't set to be open never happen). If you set the time with the other control, in the bottom right, it over-rides the passage of time completely so there is no open/close when you're using that control.