Are the days and nights exactly 12 hours long at the Equator all year?

And at what time does the sun rise and set there?

I commend you to this site, Complete Sun and Moon Data for One Day, which pretty much answers the question. The length of the day stays pretty constant, but it’s not exactly 12 hours. The atmosphere bends the sun’s rays which means the day is about 6 minutes longer than the night. (The time of sunrise and sunset varies throughout the year too, due to axial tilt and the elliptical shape of the earth’s orbit.)

There’s also the matter that the Sun has a significant angular size. Astronomers would love it if “sunrise” and “sunset” were the moments that the center of the disk crossed the horizon, but more common usage is to call “sunrise” the moment when some part of the Sun is first visible, and “sunset” when some part is last visible (at both of which times the center is about a quarter of a degree below the horizon).

The days vary some, just not as much as at higher lattitudes. The day length goes through TWO cycles per year though…They are shortest at the equinoxes, and longest (equally so) at the solstices.

Thought experiement:

Seasons occur because the earths axis is inclined with respect to it’s orbital plane.

If you mentally exagerate that tilt to 90 degrees, then you’d still have two equinoxes/year.

At the solstices, the equitorial view of the sun would be to see it circle the horizon…24 hour days.

Since the tilt is NOT 90 degrees, but only 23.45 degrees, the effect is much more modest.

I botched the above thought experiment. One solstice would see the sun parked on the northern horizon, the other it would be parked on the southern horizon.

True, but at either of the poles in summer, what you see is the sun circling the horizon (albeit not at a constant altitude) and never setting.