1. At the latitude of Stonehenge (51 degrees N), are the Pleiades (declination +24 degrees) circumpolar?
At Stonehenge, the altitude of the NCP (north celestial pole) is 51 degrees because altitude of pole = latitude of observer. So, stars have to be within 51 degrees of the NCP in order to be circumpolar, which means that they must have a declination above 90-51=+39 degrees. The Pleiades, at +24 degrees, are not circumpolar.
2. There is a total solar eclipse on December 21. What is the declination of the Moon?
On December 21, the Sun is at the winter solstice, at declination -23.5 degrees. During a solar eclipse, the Moon is in the same direction as the Sun, so its declination is also -23.5 degrees.
3. The Moon is at declination +28 degrees and the Sun is at the vernal equinox. What is the lunar phase?
If the Moon is at +28 degrees, it must be at the summer solstice point along the ecliptic. The summer solstice and vernal equinox points are 1/4 of the way around the ecliptic apart, or 90 degrees. A 90 degree separation of the Sun and Moon is the condition for quarter phase. The summer solstice point is ahead of the vernal equinox, so this is first quarter.
4. In Charlottesville (latitude 38 degrees N), what is the declination of a star at the zenith?
At Charlottesville, the altitude of the NCP is 38 degrees. The celestial equator thus makes an angle of 90-38=52 degrees with the horizon. A star on the zenith (overhead) is at an angle of 90-52=38 degrees from the equator, i.e. its declination is +38 degrees. You can see that in general the declination at the zenith = the latitude of the observer.