You will be able to tell that the moon changes it position relative to those stars. It will be easier to see the change if there are stars located on both the east and the west sides of the moon. Then try to predict how many days until the next full moon. From this, you should be able to estimate how many days it will be until the moon will be rising just as the sun is setting. You can do this for the new moon as well.
Lunar eclipses occur more frequently than solar eclipses.
Use a basketball as the earth and a tennis ball for the moon. This is not a perfect scale, but it is close. With the sun low on the horizon, try and cast a shadow on the basketball with the tennis ball. Try it the other way around.