no and yes
Yes.
Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation.
No, Earth's rotation on its axis does not cause eclipses. Solar eclipses occur when the Moon passes between the Earth and the Sun, blocking out the Sun's light. Lunar eclipses happen when the Earth passes between the Sun and the Moon, causing the Earth's shadow to fall on the Moon.
The Earth rotates in 1 day. The moon takes 27.32 days to rotate.
No. Just the opposite. The earth's rotation is slowing down because of the gravitational force between the earth and the moon. The day is getting longer by something like a millisecond (0.001 second) every hundred years.
The period of the moon's rotation on its axis is the same as its orbital period around the Earth, which is approximately 27.3 days. This synchronous rotation means the same side of the moon always faces Earth.
orbit of the moon
The law of conservation of angular momentum. The earths rate of rotation is slowing due mainly to the drag of the tides caused by the moon. To conserve the angular momentum in the earth/moon system the moon has to recede. The moon isn't moving.
27.32 days
no, they are caused by the moon, honestly
The rotation period of the moon is 27.32 days.
The Earth's rotation rate would remain fairly constant if there was no moon to affect it. The moon plays a role in slowing down Earth's rotation over very long periods of time due to tidal forces. Without the moon, the Earth's rotation would not experience significant changes in speed.