One could say:

The students in Mr Smith's art class were at their easels, looking at the sunset.

In that case, the sunset is the object of scrutiny, and it refers to the entire western sky as it is lit up by the setting sun.

But when it is used to indicate a time of day, the idiom is "before sunset", "after sunset", "at sunset".

EDIT: CopperKettle's examples on the use of "the" with a proper noun are good ones. Here are some others in the same vein; perhaps we can extract the essence from them to show when it is appropriate to use "the" with the proper noun.

I do not know you any longer! What has happened to the gentle Henry Jekyll, the Henry Jekyll with the wry sense of humor and a fondness for good port?

Get up off your ass, Jones, and get back on that horse! Where's the do-or-die Jones, the gung-ho Jones, the let-me-at-them Jones who volunteered for this mission??? I don't like this new sissy Jones who is afraid to ride on a pony just because it's a little skittish.

In your first question, we need to know if "ragini" is a proper name, title, description of a person, or ???.

In your second question, you would say

The principal asked the girls to return to the hostel before sunset.

but you could also say

The principal asked the girls to return to the hostel before the sun set.

I believe CowperKettle's answer is correct, but perhaps not clear, given the number of follow-on questions. Let me try to phrase it a different way and see if this helps.

Normally, we do not use an article with a proper noun. "Regini was the center of attention", NOT "The Regini was the center of attention."

An exception to this -- the only exception that I can think of -- is when the proper noun is used with a qualifying adjective or descriptive phrase.

Sometimes an adjective is attached to a person's name almost as a title, like TRomano's examples of "The Great Houdini" and "The Unsinkable Molly Brown". Note that if it really IS a formal title, like "king" or "president", we don't use an adjective. "King John signed the Magna Carta", NOT "The King John ..." But if you added an additional adjective that was not part of his formal title, then you would use an article. "The famous King John signed the Magna Carta."

The adjective can be a single word like that example, which normally precedes the noun, or it can be a descriptive phrase, which normally follows the noun. "The beautiful and talented Sally Jones ..." "The Sally Jones who is beautiful and talented ..."

Sometimes the adjective simply describes the person. Often we use it to distinguish the person from some other person with the same name. For example, "No, not the George Washington who was president, the George Washington who is in our math class." Or similarly, to distinguish a person at different times in his life, or different aspects of his personality. "I want to see the old Brenda again, the Brenda who was fun and romantic. I'm sick of the Brenda who is boring and nasty."

Note that an article is used when there is an "ordinary adjective", but not a predicate adjective. For example, we say, "Harold is tall", no article. But "The tall Harold entered the room", yes article. That is, when the sentence is simply stating that a person or object has this attribute, using a word like "is" or "seems" or "becomes", we don't use an article. But when the description is attached to the person in the course of saying that he did something else or something else was done to him, then we do use the article.

Let me add that the article in such a case is usually "the", but not always. And all my examples have used people, but you could use anything that is identified by a proper noun. Like, "I remember an America very different from the country we know today."