Kaito was killed when a guy pushed him off a roof. The pusher lived.
~Kensei pushed Kaito off of the roof and walked away
Peter and Nathans dad commited suicide and had made multiple attempts at it.
~Kensei can survive suicide attempts
The Killer is also the boogyman
~No, Kensei and Parkmans father are in kahoots
In the photo of the 12 (39 min 19 sec in ep 2x04 of my copy) assuming that Nathan and Peters father is opposite Kaito from their mother (face turned to side) he is a proper match for height/weight of Kensei.
~Kensei is therefore Peter/Nathans father, the killer, and Claires grandfather.
Theories:
At some point Hiro comes back, bringing Kensei with. This may be done to fake Kenseis death after completeing his mission and saving Japan. I will go even further to speculate they teleport when destroying the guns in a huge explosion. Hiro, distraught by the death of his father, goes back in time to see him and leaves Kensei with him (would be proper age to support his fathering Peter/Nathan and marrying Angela). Hiro then goes back to the present and realizes he has killed his father by bringing Kensei back. Vowing not to tamper with the Space/Time continueum anymore he hunts down Kensei and confronts him. Maybe he kills him with the virus the company is going to create....

this show

