First of all, I think Kai is really smart and totally chilled out (Unless someone mocks his cats or Max, Rei, Takao, ect) and he'd be really stern with them most of the time.

Kai is like a dad to the team, he's the voice of reason..Or tries to be, since he's grown up he's tried to be less harsh but it usually comes out stuttering and awkward. 

He tries to be cool but it fails. (Scarf getting caught in doors, you know how it is)

Also I said this but I see him being gay or not wanting anyone at all. He's be SO WEIRD ON DATES. Someone would call him handsome and he'd sit there like "Wow..Uhm..You're alright..I guess?" but he'd find people attractive but it'd take him a long time to be in a relationship and if he rushed into one he'd instantly regret it and go to Rei/Max for help.

He secretly hangs out with Max, and spars with Rei.

HE LOVES PUNS. Especially about fire.

Which reminds me, he burns things when he's embarrassed. 

He can't cook at all, everything BURNS.

He's a witty guy, always out smarting the group. 

Him and Yuriy have a strong friendship and he still respects his old team. 

He's very..quiet? Doesn't say much, doesn't type much.