Final answer:
At the equator, stars rise almost exactly in the east and set almost exactly in the west option (1), but not all stars would be visible every night. The North Star would be on the northern horizon, and over the span of a year, nearly all stars would become visible due to Earth's rotation and orbit.
Step-by-step explanation:
If you were at the equator, you would see stars rise almost exactly in the east and set almost exactly in the west. Stars that rise due east would not go directly overhead unless they were on the celestial equator; rather, they would arc across the sky.
The celestial equator would indeed pass directly overhead. Point 2 is incorrect: the North Star, or Polaris, would not be directly overhead; rather, it would be on the northern horizon. As for point 3, not all stars would be visible every night; the stars you can see would only be those that are above the horizon at night.
For point 4, stars to the north and south both rise in the east and set in the west; they don't reverse as stated. Stars move straight up from the east side of the horizon and set straight down on the west side. At the equator, you don't have a single night during which every star is visible, but over the course of a year, nearly all stars are visible because of Earth's rotation and orbit around the Sun.