Earthquakes

Earthquakes, volcanism, and hydrothermal features go hand in hand at Yellowstone. The underground plumbing of hot water and magmas beneath Yellowstone is influenced by the same stresses that cause earthquakes.
It isn't that simple. There is not one magnitude above which damage will occur.
There are a few historic examples of simultaneous eruptions from volcanoes or vents located within about 10 km of each other, but it's very difficult to determine whether one eruption might have caused the other.
On January 19, 1968, a thermonuclear test, codenamed Faultless, took place in the Central Nevada Supplemental Test Area. The codename turned out to be a poor choice of words because a fresh fault rupture some 1200 meters long was produced.
The USGS has some great science fair ideas related to earthquakes. Find inspiration for projects on other science topics by browsing the USGS Education website.
Geothermal energy (heat energy from the Earth's interior), is used to generate electricity in a variety of places throughout the world.
No. Neither the USGS nor any other scientists have ever predicted a major earthquake. We do not know how, and we do not expect to know how any time in the foreseeable future.
Scientists agree that drilling into a volcano would be of questionable usefulness. In addition to the enormous expense and technological difficulties in drilling through hot, mushy rock, drilling is unlikely to have much effect.