Hi! 
Sorry for making you wait, I wanted to reread parts of the book to “fact check” some stuff, but haven’t had the time to do so. But I figure I could just post the thoughts I had, anyway.
Hidden due to length of spoilery stuffs
So we have four characters whose whereabouts are a bit of a mystery: the professor 天王寺 翔蔵 (ca. 80 years old), the author 天王寺 宗太郎, the architect 片山 基生, and Noboru’s father 鈴木 彰.
My theory is that Akira was the one who died in the car accident 12 years ago, not Soutarou. I think we’re probably all on the same page on that one, right? So when Kimie told Saikawa that she received a phone call and the manuscript from Akira, that must have been a lie. I think it was Soutarou himself who sent that manuscript after having finished writing. (Though one might wonder why the writing style didn’t resemble his usual writing style… 
)
He supposedly stayed with the professor in the basement for at least four years while writing that manuscript, I think? And then killed himself, but from the hint about the title and stuff, we know that the skeleton has to be the real professor. Maybe he died by natural causes, either way Noboru and the “professor” carried him out to the woods to hide the body. Was this while Noboru was still in middle school or maybe a bit later? From the visit at the hospital we know that while he was in middle school, Noboru heard from the “professor” that he was his real dad. Maybe that was Soutarou who pretended to be the professor. Could also have been Katayama Kisei if my theory is wrong.
In chapter 4, part 6:
The fact that Saikawa watched Katayama Kazuki and Suzuki Noboru playing billiards and thought, “huh, they look very similar in appearance”. So maybe they have the same father? 
Katayama Kisei?
Even if it doesn’t work out timeline-wise, maybe Kimie and Soutarou (who seemed to love each other) were secretly together even back then. She was angry at Ritsuko for being Soutarou’s wife and also angry at Ryouko when she found out Soutarou actually liked Ryouko too.
While Noboru was still in middle school, he heard directly from the “professor” that the professor was in fact his real father. I don’t think he never heard Kimie talk about it. And I don’t know if this makes sense (I’ve kinda forgotten the timeline), but maybe the professor had already been “switched out” by the time Noboru learned that fact during middle school.