The (lack of) fighting in Kampfer (as of episode 4)
All of the Kampfers are theoretically ordinary highschool kids who basically got drafted against their will. It feels entirely right that they are generally unenthusiastic about actually beating each other up, or even theoretically killing each other, regardless of what the Moderators may want them to do, and that they would much rather hang out and talk with each other (and, in the case of Shizuku, yank everyone's chains). If anything, they now have more in common with each other than with their classmates.
(This makes me unconvinced that Akane actually is as terrible a shot as she seems to be. It doesn't even have to be deliberate and conscious on her part. Really, humans are startlingly kind when you get down to it; outside of cliched shounen action series, you usually have to work quite hard to get them to hurt and kill each other.)
As for Akane: I think she's just manic (okay, very enthusiastic). Shizuku is just an excuse to let off some energy, as Natsuru was at the start of the show.
(I believe that Akane even more or less admitted that the reason she stopped fighting Natsuru wasn't that they were on the same side but that she didn't have the heart for it after he saved her.)