As for Valeris "cold bloodedly" killing the 2 assassins, I do not believe that the character was that kind of a killer, at all. I wouldn't call a soldier firing his weapon on the battlefield a cold blooded killer. Even if he used his bayonette on The Enemy, I'd be hard pressed to call him that. She killed because it was logical and necessary to the conspiracy plot. She killed in the line of duty, as a soldier would, if ordered to. In fact, when she creeps up on Spock in Sick Bay, I know she's trying to be "careful," but there's no sense of urgency, either. It's almost as though she doesn't want to do it. That's my perception, at any rate.
In other words, if she could've gotten away without killing anyone on ENTERPRISE, whilst still supporting the assassination of Gorkon with falsifying the databanks, she wouldn't have looked for an opportunity to kill anybody. But it would've helped to know why she bought into the conspiracy, though. What she was afraid of. As to prosecuting Kirk & Bones, the Klingon Chancellor's daughter isn't overly surprised at Kirk being freed when she sees him at Kitomer. What that's about, I don't know. But I would've demanded he get sent right back to that penal asteroid, whatever happened. That part always bothered me ...