I don't know if someone already answered that, but I don't have time to read the rest of the thread now, so, my theory:
Against Kaladin: Nalan is strong, but he is not invincible. Maybe he realizes Kaladin could beat him, if a 13yo girl can escape him and his men. Or maybe that has something to do with the fact that he is a slave, killing him would be destroying someone else's property, or that the bridgmen cannot be executed by anything else than refusing to charge at the parshendi, so he could not get authorization. Nalan appears to investigate the person thoroughly before taking action, he couldn't kill him right away;
Shallan: I doubt it would be considered homicide, it was self-defense and defense of others. He could, however, have come after her under the accusation of stealing Jasnah's Soulcaster, but even her (Jasnah) didn't know about what happened until the day of poisoning, and then forgave Shallan right after (thus dropping the charges). Also, the law of Alethkar wouldn't allow the execution of a lighteyes just for theft, so Nalan wouldn't be able to get authorization for this;
Jasnah: The book makes it very clear that everything she did in that event was completely legal.