Answer to Question 1
An eclipse can occur only in a period called an eclipse season, during which the Sun is close to a node in the Moon's orbit. For solar eclipses, an eclipse season is about 32 days long. Any new moon during this period will produce a solar eclipse. For lunar eclipses, the eclipse season is a bit shorter, about 22 days. Any full moon in this period will encounter Earth's shadow and be eclipsed.
Answer to Question 2
The Sun must be near one of the two nodes of the Moon's orbit, and the Moon must pass near either the same node (solar eclipse) or the other node (lunar eclipse).