What Ken does when I'm not playing him...
Well. Every day Ken goes for a run. It's not always at the same time, but he does make sure to run/work out every day. He tells himself it's just to keep in shape and for his soccer game, but the truth is he's sticking as close as possible to the regimen he kept as an assassin. And he's a little too scared to think about why. Maybe part of him knows he'll wind up going home eventually.
The past month or so, he's also been trying to do some focus-practice every day... blanking his mind sorta stuff, to help him with the violence problem. But he forgets a lot.
He has a lot of off-screen soccer games with Clark and Yousuke, so I figure it's safe to say he tracks down someone to play every few days, at least. Other days he stops by the greenhouse... he actually misses being a florist. Have you noticed he jumps at the change to arrange flowers for people? It's like crack, apparently. And while we're on extracurriculars, he misses his motorcycle. Someone needs to show him the holodeck.
...and if anyone cares, he eats in the mess hall, and probably makes another stop or two in daily. Unless someone's offered him food that day. Ken never turns down food, not that it's really important.