[Used Can]

I can see what's actually happening.

Ikusa is Himegami, who (just as Hayate) went back in time for unknown reasons and met Yukariko. They fell in love and had a child. Eventually, he had to return to his own time (a few years later), and that's how Nagi's father "died". After Yukariko died, Ikusa changed his identity and picked up the name (surname?) Himegami in order to look after his child. Shit happened and he had to leave.

Oh yeah...