1. At what time does the full moon rise?

The full moon rises at sunset.

2. When does a lunar eclipse occur?

A lunar eclipse can only take place at a full moon, and only when the moon passes through a part or completely through the Earth's shadow.

3. Define:

Umbra

Umbral Lunar eclipses are when the Earth blocks the entire sunlight of reaching to the Moon. So basically during the Umbral Lunar eclipses no solar rays are able to reach the moon. Around 35% of the Lunar eclipses are Umbral.

Penumbral Lunar Eclipse

Penumbral Lunar eclipses are when parts of the sun's rays are blocked by the earth, of reaching the moon However not all of the rays, so basically, on a Penumbral Lunar eclipse, parts of the sun's rays are able to reach the moon.
Around 35 % of all the Lunar eclipses, are penumbral eclipses.

4. If Luna orbits the Earth every month, why don't we have a lunar eclipse every month when the Earth is between the Sun and Luna?

We don't have a lunar eclipse every month because the Luna's orbit around the Earth is actually tilted around 5 degrees to earth's orbit around the sun. This explains that the moon's movement is generally above or below the earth's orbit.

5. How would a total lunar eclipse look to an astronaut standing on Luna?

An Astronauts standing on the moon during a lunar eclipse, would experience the Earth eclipsing the sun. The would also observe a very great and bright red circle around the Earth.

6. What color does Luna look during the eclipse? Why?

Astronomers haven't been able to discovered actually how dark the
Moon is during total/Umbral eclipses. However what they have been able to discover is that the colour during eclipses can differ from a dark greyish or brown, to a reddish or a light orangeish colour. The colour of the moon during an eclipse can also depend on the amount of dust in Earth's atmosphere.

7. Sketch the position of the Sun, Luna and Earth during a lunar eclipse. Include the umbra and penumbra.

8. Go to http://tycho.usno.navy.mil/vphase.html to find out the phase of the moon when you were born. (Use universal time. 0 hours = 0:00, 4 hours = 04:00 etc.)

Date: 30th September 1988 08:00
Phase: Waning Gibbous

Sources/Links