I'm really confused about the correct usage of dusk and twilight. Can we use them to describe the time before night falls or day breaks?
This is actually an interesting question, since they aren't quite synonyms as one might imagine. Here's what a bit of research produced:
The casual difference in definition is as follows (via Wikipedia):
Twilight is the illumination of the Earth's lower atmosphere when the Sun itself is not directly visible because it is below the horizon.
Dusk is the darkest stage of twilight in the evening.
However, there are 3 more rigorously defined types of twilight and dusk — civil, nautical, and astronomical. Here are the distinctions (via timeanddate.com):
Civil twilight occurs when the Sun is less than 6 degrees below the horizon. In the morning, civil twilight begins when the Sun is 6 degrees below the horizon and ends at sunrise. In the evening, it begins at sunset and ends when the Sun reaches 6 degrees below the horizon.
Civil dusk is the moment when the geometrical center of the Sun is 6 degrees below the horizon in the evening.
Nautical twilight occurs when the geometrical center of the Sun is between 6 degrees and 12 degrees below the horizon. This twilight period is less bright than civil twilight and artificial light is generally required for outdoor activities.
Nautical dusk occurs when the Sun goes 12 degrees below the horizon in the evening.
Astronomical twilight occurs when the Sun is between 12 degrees and 18 degrees below the horizon.
Astronomical dusk is the instant when the geographical center of the Sun is at 18 degrees below the horizon. After this point, the sky is no longer illuminated.