Thank you so much for your time and explanation, Richard.

Have a good day.

Terecia

The long sentence "Before this Fall semester..." is a quote from something that was written, hence the quotation marks showing that it was reported speech/writing. Yes, it's very formal, perhaps more formal than it needs to be. It was written by someone at a university. I think they need to take a course that will teach them how to say something in as few words as possible, for example,

"Before this Fall semester, students had readily available access to withdrawing themselves from the university completely with no ifs, ands or buts."

Students could withdraw from the university before the beginning of the fall semester with no questions asked.

Yes, 'ifs, ands, and buts' is usually a final closing statement, like saying "Do what I tell you to do, and don't argue/don't question what I say"

May I ask you one more question regarding the sentence you gave?

--> Before this Fall semester, students had readily available access to withdrawing themselves from the university completely with no ifs, ands or buts. 

(1) Is it a reported speech? It seems too formal.

(2) It seems the phrase "no ifs, and, or buts" mostly put at the end of a sentence, isn't it?

Terecia...

This expression has several uses, although it is not used very frequently anymore.

"No one should leave the room without ifs, ands, or buts before I dismiss the class."

No one should leave the room before I dismiss the class, without ifs, ands, or buts.

No one should leave the room before I dismiss the class, and no one should argue or question my instructions to you.
No one should leave the room before I dismiss the class, and you cannot debate or argue against my decision.
No one should leave the room before I dismiss the class, and you must do what I say without any discussion.

More Examples

Before this Fall semester, students had readily available access to withdrawing themselves from the university completely with no ifs, ands or buts. (no opposition to withdrawing/no questions asked)

The new boss said that if we're even one minute late, we'll be fired—no ifs, ands, or buts.  (no excuses for being late will be allowed)

We're definitely going to lose our jobs after this merger, no ifs, ands, or buts about it.  (there is no doubt that we'll lose our jobs)

Make sure you're at your son's party tomorrow—no ifs, ands, or buts about it!  (no excuses allowed - you must attend the party)

No ifs, ands, or buts—just do as I tell you!  (don't question my orders - just do as I said)

Thank you for your precious corrections, Richard

As for the sentence # 3, can I say:

No one should leave the room without ifs, ands, or buts before I dismiss the class.

    This is the first time I've ever heard the phrase ifs, ands, or buts. And, I'm glad that I could make two correct sentences out of three. English is fun and complicated as well.