It is because of this that I am compelled to provide my thoughts on your translation. Most will be phrased as questions, but the rest will be simple quips or nitpicks.
Chapter 1
Was the line supposed to trail off like that? I know it's supposed to finish off as "rest of the world", but it feels just a bit odd...Mikoto: Everything here is state-of-the-art, thirty years ahead of the rest of the...
I was thinking of "all the way from the classrooms".Mikoto: You could hear it all the way in the classrooms?
Was the title rendered as "Star"? There might be a card motif hidden here if it was "Ace", considering that another known title in that place is "The Queen".Kuroko: You're the Star of Tokiwadai!
I didn't know that Kuroko believed in something while in a city that has no religious structures.Kuroko: Dear God... What's with the face mask?
I think "teleport them inside your body" flows better.Kuroko: If you continue to resist, I will teleport them inside of your body.
Chapter 2
Not "such misfortune"? Eh, I won't argue this.Touma: I have no luck!!
Chapter 3
"Try to help"?Mikoto: If someone did try and help a complete stranger...
"Well-bred", maybe?Touma: She might look well bred, but she's hardly mature.
Chapter 4
Another believer. Huh.Uiharu: God, Saten-san! There are boys here!!
Maybe "show you mine as an apology"?Saten: I could show you mine by way of apology.
Instance three of a believer.Saten: God, you work way too much.
As much as I like how you rendered this term, his and Komoe's Japanese VAs pronounced it as "An Involuntary Movement".Teacher: AIM stands for "An Involuntary Motion"...
Referring to shrink-wrapped stuff?Mikoto: You know what? I hate it when magazines are in bags, and you can't just read them...
Chapter 5
Implying something here?The main character of A Certain Magical Index.
Chapter 6
"First-year"? "Freshman"?She is a first year student at Academy City's prestigious Tokiwadai Middle School
Thanks for the names.Kawazaki
Domura Jintou
Morimoto Futari
Chapter 7
No comment.Bald Thug: Who the hell do you think you are?
Terminology
Regarding "psychic" being used to refer to those with powers (not complaining about "psychic training"), I'd like to hear your thoughts on this decision. I'm assuming you passed on "esper" for similar reasons.
Regarding "Level Zero/One/.../Five", was there a reason as to why they aren't rendered as "Level 0/1/.../5"? If it's because it's being spoken, I understand.