At the age of four, the narrator's mother bought him a murder mystery in which five people are killed. FOUR? Even if he was a prodigy, it seems like a strange thing to give him.
Let's look at the timeline:
1908 - Masahiro Junsuke born
When Masahiro Junsuke is young, his wife cheats on him, has a son. The lover dies in the war later.
~1929 - Seguko born
1931 - Victims all born this year, roughly
1933 - narrator given book by mom
1933 - Narrator's parents killed ("15 years ago")
1941 - "The three of us have been together since we were twelve" -- Zephan, Naito, Seguko
1944 - narrator stationed in Korea at age 15
1945 - narrator returns
1948 - present day (3 years since return from Korea)
The mystery's author is 40 years old. His wife cheated on him with another man when he was young. That could potentially give a kid the age of Seguko or the victims. Let's go with this:
Alibi or no alibi, the students would have become incredibly suspicious of any teacher who wanted to be alone with them after the first murder or two.
However, a student who was well-liked, charismatic, and capable of getting the names of all of Chika's recent contacts?
The culprit is the final victim, Meruko.
Seguko (who she edits for) and Naito (her brother), are absolutely obsessed with murders. Furthermore, Seguko is obsessed with the works of Masahiro Junsuke, and Meruko is the only girl in his life, to the point where he mentally conflates her with the doll-victims of [The Smiles of Heaven]. Based on his writing and subtle cues, she is aware of this.
While in theory her school interactions might give her a respite from this environment, Masahiro Junsuke and serial murders even come up there, as Clair pushes his books at her. This leads to an obsession.
Eventually, she found out - or perhaps merely started to believe - that her mother was Masahiro Junsuke's wife, and that she was the child of infidelity whose existence led to Masahiro's bleak writing. She formed a fantasy in which she was the controlling narrator of [The Smiles of Heaven], making girls smile.
She chose victims to match her age. The "Mom, Dad" lines in [The Smiles of Heaven] suggested that the killer in that story was young, too, and killed "friends."
The "Mr. Detective" notes were an added flourish to get her brother's attention, based on when she heard Winter use the term; it was both a blind and a taunt, meant to deflect attention towards Winter.
In the end, she even did what the narrator of [The Smiles of Heaven] was implied to have done... and cut a smile into her own face.