«"I would like to hear an explanation» –," said Princess Celestia to her prized pupil, Sunset Shimmer.

That punctuation isn't used in English.

Sunset was young, confident, and (had a tendency/tended) to overestimate her own abilities.

She was the best student in Canterlot school; her talents mesmerized teachers and classmates; s. She was a ways beyond everyone onelse at school.

"A ways" is informal speech, but I thought you might have heard it before and wanted to write it. Otherwise, you can just say "far".

However, there was a problem –: she couldn’t make friends.

A dash (--) might be fine but I think a colon (:) is better.

After a short talk with her mentor, she said this: «"How can I make some friends if I can’t talk to them about someanything, or even approached them,? I don’t have a plan, or a tip to do that! »clue, on how to do it!"

"I wouldn’t jump to conclusions if I was you.

Friendship can’t be determined by plans, or a couple of tips,clues-- it’s an experience, y. You need to try, to feel it, to feel others and their emotions. –," replied Celestia.

«"But I can’t, if they asksay or do something or behave unexpectedly?

I mustneed to know how to reply in such situations! »spond to that!"

Celestia followed her with her eyes, a note of sorrow was in her gaze; s. She thought about what if shecould happen if Sunset really overdid it with her studying her, s. She needed to make her own decisions, and stop looking for answers to every question in books, m. Maybe she'd finally understands it, or she needs me for herhelp to understand.

Sunset walked to the library; library a. As always, it was crowded with ponies –-- someone sitwas sitting on the table with a huge big, it seemed that she wook, seeming as riveted with athe story like story was aas if it were made of glue;. A flickering light was litlit the pages onf her book.

She caught herself she wondereding about something for 5five minutes.

Numbers should be written out in stories.

She picked a book from the bookshelf and smelled theits soft cover of book, then she came, then went to the table which was inat the edge of the room.

Then, an amazing thought suddenly hitpopped into her head –: what if Celestia was wrong, and the answer forto her question really laid indid lie in the books in this library?

A big smile appeared on her face aftert thate thought.

Sorry for lenghth :)

«"I would like to hear an explanation» –", said Princess Celestia to her prized pupil, Sunset Shimmer.

Sunset was young, confident, and had a tendency to overestimate her abilities.

She was the best student in Canterlot sSchool; her talents mesmerized teachers and classmates;, and she was a way beyond everyone on school.

After a short talk with her mentor, she said this:, «"How can I make some friends if I can’t talk to them about something, or even approached them,? I don’t have a plan, or a tipway to do that! »"

I wouldn’t jump to conclusions if I wasere you.

Friendship can’t be determined by plan, or a couple of tips, - it’s an experience, you need to try, to feel it, to feel others and their emotions. – replied Celestia.

«But I can’t, what if they ask something or behave unexpectedly?

Then, Sunset left and went to the library, wondering about Celestia’s words.

Celestia's eyes followed her with her eyes, a note of sorrow was in her gaze; s. She thought about what if she really overdido it with studying her,- she needed to make her own decisions and stop looking for answers to every question in books, maybe she finally understands it, or she needs me for her to understand.

I feel like the last "maybe she finally understands..." might be a bit redundant, and it's already clear what she might understand. I think the rest of this sentence is great though!

Sunset walked to the library;. The library as always was crowded with ponies – someone sit on the table with a huge big, ismile. It seemed thatlike she was riveted with a story like story was a glueby a story; flickering light was litlit the pages onf her book.

I'm not entirely sure if you meant "huge, big smile" or something else. "a story like story was a glue" makes sense, but sounds a little clunky in this context. Something like "she couldn't put the story down" might be a more idiomatic way to express this?

She picked a book from bookshelf and smelled the soft cover of book, then she came to the table which was in the edge of the room.

Then, an amazing thought suddenly hit her head – what if Celestia was wrong, and the answers for her questions really laidy in the books in this library?

Since she had multiple questions, I think it makes sense to use plural here.

Sorry for lenghth :)