The reason we on Earth have equinoxes at all is because the Earth's axis is tilted. ... Earth's axial tilt also means that our planet's equator is tilted relative to the plane of its orbit around the Sun – what astronomers call the “plane of the ecliptic”.
As the sun rays fall straight and two halves of the earth can be made through equator,it represents the equal effect on both parts so,day and night are equal in equator.
Mountains wouldn't not be mountains. If the world was flat, then that would necessarily mean that the tectonic plates won't shift or rub up against each other.