3. The moon takes about a month to orbit the Earth.
Even though the moon rises in the east and sets in the west daily, it also moves on the dome of the sky every day due to its own motion in orbit around the Earth.
This motion of the moon is slower and not very noticeable. It moves in front of the fixed stars. If you take a look at the moon at night and look at it again after a few hours, you'll notice it has moved towards the west. That westward motion is brought about by Earth's spin.
You can also detect the moon's orbital motion at night too. But you'll have to closely watch the moon, with respect to stars in its vicinity, for many hours.
It is easier to notice the moon's eastward orbital motion from one day or night to the next. It looks as though the moon is moving on the inside of a circle of 360 degrees. The moon's orbit takes it around Earth's sky once a month, because it takes the moon about a month to orbit the Earth.
With regards to the fixed stars, the moon moves by about 12-13 degrees daily.
4. The Moon moves eastward.
The moon moves another 12-13 degrees eastward on the sky's dome each day. The Earth rotates a little longer to bring you around to where the moon is in space. Therefore, on the average, the moon rises about 50 minutes later every day.
As the rising time of the moon becomes later and later, it causes our world to show up in a different part of the sky every night for at least two weeks between new and full moon.
Two weeks after the full moon, the moon rises later and later every night.