I have small understanding of Japanese myself, so I might be explaining each chapter inaccurately. I also forgot a lot of certain parts of chapters (especially Chapter 2) and how the "App" basically works story-wise.
Well, here I go. Behold major spoilers for the main story.
Tutorial and Chapter 1 is basically about the Protagonist finds themselves in Tokyo, then meets Salomon-kun (Yes. The -kun part is apparently a part of his name as well), who acts as someone who explains things to the Protagonist about the world's mechanism (and apparently time stops everytime you interact with him, as Salomon-kun only talks to you), and is interrupted by Ryouta who's currently getting chased by a Red Oni. Both the Protagonist and Ryouta makes their way to the school and meets Shirou and Kengo there. The Protagonist is then welcomed into the school by the teachers.
Chapter 2 is focused on Shirou as he is trying to cope with his rather chaotic magical powers that makes him capable of summoning a bunch of demon creatures, paired along with the very idea about having to battle and cause bloodshed with his powers. The Protagonist's role here is to help Shirou cope with those issues.
Chapter 3 is somewhat focused on Kengo, as the Protagonist has a lot of interaction with many other characters here (especially Horkeukamui, Magan, Bathym and Andvari.).
One day, Kengo never came to the school, so the Protagonist and Shirou searches for him in the Toshima area to make him go back (he's found street-fighting in there and refuses to go back). The Protagonist ends up meeting members of the Ikebukuro Bersekers and participating in battles against most of their members to get Kengo back, while Shirou investigates with Duo and Shuuichi.
I might do the current Valentine event story as well. I just need to re-read them, since the fifth one cracked me up.