Yeah, I think some kind of "basic training" session with them getting a first sense of how to use their powers together could be really fun!

On the hang-out front, Shindou is...not the most independently sociable sort? So, he probably wouldn't be the one to go out of his way to encourage everyone to hang out or go for a weekend trip into the city or whatever. But he will be big on everyone bonding, so if someone else suggested it he'd probably encourage everyone to go along and/or spring for cab-fare.