Kayo's usually dressed in red, most prominently in her jacket. Have you ever thought why she chooses to wear so much red? Red is used on stop signs and car/bike reflexes because it's the one color people notice the most. If you remember the scene where Satoru checked out her class profile, that is, the one where she wrote a short story about being alone on a faraway island, it's clear she is calling out for help, even if she doesn't realize that consciously. Satoru even says it was a red flag himself. After all, for such an introverted, shy girl that hangs out alone all day and doesn't tell others about her problems, doesn't it seem strange that she always wants to wear red; the one color that is guaranteed to draw attention to herself, instead of colors that make her blend in with the background?
When shopping with Sachiko, Satoru endures multiple reruns (condensed to one in the anime), but is confused when it stops even though nothing he's done has actually solved anything besides get his mother to notice and recognize the kidnapper, which results in her death. But it did actually fix things in the broader sense, by inducing Sachiko's death, which constituted enough of a disaster for Satoru to turn back time and prevent the killer in the first place.
Actually, it also solves the immediate scene, as Sachiko later ponders that her noticing the kidnapper caused him to cancel his plans and leave without the victim.
In the OP, right after the blue-tinted shots of Airi, Sachiko and Kayo with Satoru in the back, there's a flash of red. If you manage to pause it there, you will see a bespectacled man where Satoru was. Who is this man? None other than Gaku Yashiro, whose presence as the murderer is represented by turning his eyes a striking shade of red.
A fan familiar of mystery would have questioned why the police never bothered with checking the finger prints on items to further solidify the proof that Yuuki and Satoru in the original timeline are the murderers but then you realize that the story also focused on psychological impacts, which makes why the police didn't bother checking further to be more sensible. People, in general, judge things based on how they see it than to judge them based on what really happened. The quote "Never Judge A Book By It's Cover" truly had been deconstructed in a realistic setting. And also a case of Truth in Television.
Actually, in the manga they do check physical evidence, and there is usually at least a small amount tying it to the patsy, e.g. there were Satoru's finger prints on the knife used to kill Sachiko.
If one remembers the information Satoru gave in Episode 1 pertaining to his Revivals, he mentioned that whatever he does, the world seems to balance itself out. Sometimes this rebound hits Satoru himself, as was shown he lost three days by saving a child. This neatly framesSatoru's 15-year coma. By saving three children eighteen years in the past from certain death, he suffered the rebound. This is further enhanced by Kayo and Hiromi's marriage and child, Mirai, whom he more or less butterflied into existence by saving both of his parents.
Changing something through a revival doesn't necessarily send Satoru back to the future in a flash. Normally, the revival is short enough that it doesn't matter, but his revival after Sachiko's death takes him back eighteen years, and he still mentally considers himself a 29-year-old adult in the body of a child. Preventing the murders won't change the fact that he might have to spend the rest of his life eighteen years older than he actually is and spending the following years knowing more about the future than he'll be able to tell anyone. Ending up in a fifteen-year coma and being put back in a body to match his functional age might not have been such a bad thing after all.
As Satoru has been in a coma in the new timeline all of his original revivals have been erased, everyone he saved from whatever situations they were in before he jumped back to 1988 have lost their savior. (eg Who saved the kid from getting hit by an out of control truck in episode 1 of the anime if Satoru was in a coma this time?)
Satoru actually wasn't in a coma at point (Ep 1 is in 2006, he wakes up in 2003) but he does mention that he never has another revival again which does suggest that everyone is left to their original fates now...
On the other hand there's a chance that a revival was no longer needed, after all the sheer fact that Kayo, Hiromi, and Nakanishi are now alive and active in this world. Their presence could be enough to stop or save whatever the revivals were about. Maybe one of them saved that child in episode 1.
Also, with Satoru's memories restored now, he effectively knows what is GOING to happen in each incident that he originally experienced a revival, and can take steps to prevent them (probably much earlier this time around).
Considering the revivals started after Kayo's murder it's possible they all represent down-stream effects of things going wrong in the timeline secondary to that. When Satoru finally has a chance to go back and fix the original insult to the timestream the revivals stop because they are no longer needed because those people are now (due to some butterfly effect) never in danger in the first place.
Considering both of the Yashiro brothers turned out to be massive sociopaths, it makes you wonder just how bad their parents were.
In the manga, Kenya figured out who the killer was after Satoru almost drowned and it's entirely possible that he figured it out before Yashiro quit being their elementary school teacher and left town, meaning Kenya had to go to classes taught by the person he suspected of attempting to murder his best friend, and of being a serial killer
The Killer's original plan to frame Satoru for his mother's death had quite a few holes in it. While the killer was said to have memories Satoru's work schedule, the timing he conducts the murder would have still conflicted with the timing as any autposy report report would've shown that Satoru could not have made it home in time at the time of his mother's death.
He was probably planning to get away with it somehow, trusting that killing more people would lead to his good future anyways thanks to his power.
Sachiko was killed, at most, five minutes before Satoru arrived. An autopsy would not reveal her time of death to that level of precision. If anything, the fact that she clearly died very recently (as opposed to an hour or more before Satoru got home) would only support the assumption that Satoru killed her right after he got home.
. Who is this man? None other than Gaku Yashiro, whose presence as the murderer is represented by turning his eyes a striking shade of red.