I’ve read your story and made it to the end. Which is good for me, I don’t often manage. Clearly it was easy to ready, which is good. However, I have a few pointers that I believe will help.

Your first line is a little confused in that sensei addresses the class and then the two new students with nothing to indicate that she’s changed from addressing one to the other. As it stands, it reads as if the class is being asked to introduce themselves.
This is easy to fix!
"Everybody, we have two transfer students that will be joining our class,” said Sensei. She turned towards the new students and motioned for them to come forwards. “Please introduce yourselves.”

“I wasn't much of the types of person who paid transfer students much students came every year[…]” This sentence is confusing and I’m not sure what you’re trying to say. For a start, you should avoid using the word ‘much’ twice. Read it aloud to yourself and see what you think. Also, I do feel the entire third paragraph is somewhat superfluous. I would cut it. Also, passed is the past participle of pass. If he/she past a test, it’s implying they walked past it, not passed it.

Try not to say more than you need to, Heave a read through what you’ve written to make sure you never repeat yourself.

“I hadn't really been paying attention, but in the next moment, the seat next to me had been taken by Katsu. Akane had taken a seat next to Katsu. A lot of disappointed girls pouted at me. It wasn't my fault [the new kid decided to sit next to me. – You’ve already said this]”

“I walked into room 313. That room used to be a class room, but now was used as a storage room. Technically, I didn't have permission to go there, but I liked being alone. No one ever came in when I was in here, so now it was more of my own private lunch spot. [I entered the room-you’ve already said this ‘I walked into room 313.’] and took out my sandwich from my backpack.”

Take out all dialogue attribution adverbs!
You use eagerly, playfully, matter of factly, half-heartedly and mockingly. Now, I understand why you have them. You want your reader to know how the words are being said and the emotional state of the speaker. However, over-using adverbs isn’t considered good writing. The reason for this is that the reader should already have an idea of how the character is speaking the words. This can come from what they know of the character (if they are broody or playful for example) and also through the words themselves.

E.g.
"The moon completely orbits the Earth about 27.3 days," Katsu said matter of factly.
Katsu would say it matter of factly, because it is a fact. Just stick with ‘said Katsu.’

Also, italic can be used to stress words. But do this sparingly.

"Yes, ma'am,"
Reads differently to
"Yes, ma'am,"

Also,

"Well, can your highest quality, brand new detector be more specific of where he might be?" Katsu asked mockingly.

Could be:

"Well, can your highest quality, brand new detector be little more specific of where he might be?"

Again, like I said, use italics sparingly.

The best advice I can give you is to make sure that every word is relevant. If not, delete it!

I hope this helps and happy writing!

Awesome! Cant wait to read more!