What is the reason for Earth's tilt sideways to the sun and hours of daylight and darkness in both hemispheres on about March 20?

Part A) The tilt was caused by the combined momentum of all the fragments that came together to form the Earth. The most significant of which was probably the collision of the large planetoid that formed the moon.

Part B) 12 hours each, due to the fact that the Earth's axis is aligned with its orbit on the equinoxes.

The earth's axis is never aligned with the earth's orbit. It is inclined at about 67 degrees to the plane of the orbit, and this never changes.

The earth's axis has to point somewhere, and it happens to point towards some insignificant star which everybody therefore calls the pole star. This direction of the axis of spin does not change significantly over anyone's lifetime. At the equinoxes (= equal day and night) in March and September), this axis of the earth's spin lies exactly at right-angles to the line from sun to earth (the sun appears to be on the horizon all day at both poles, for the whole day). As the earth spins on those particular days, everywhere not at the poles sees the sun for exactly 12 hours.