If I recall correctly it was stated that he had killed before and did so after this series of crimes. The "obssesion" with Kayo may be that he is just plainly psycho and its his target cause she fills some characteristics and had a plan to do his "thing" with her. Most serial killers choose victims and stick to them even if they get an easier target/chance with some1 else.

He knew they left her alone in the shed and planned along for the 2nd time murder (she is no longer staying alone in the park, 1st time murder) so he should be planning a 3rd time murder. If he knew she was in the bus he would have done a new plan based on that info and not ruining this new chance.

Yuukis alibi would work for the night the window was broken and the father (and neighborhood) woke up and made a ruckuss. The night the killer went into the bus was another one.

I still have troubles with the smart friend. He is too fking clever, composed, methodical, considerate. We can assume that just happens to be a normal functioning genius (part of that 0,1% of population) to be there by sheer luck (and didnt skip grades cause whatever) but im not buying it. ¿What if Sastoru isnt the only with the power of going back in time?