I know Im not allowed to kill Player Characters without the Players permission, but what about someone elses NPCs?
That depends on the situation. Some NPC’s take the form of gangs of attackers or hordes of monsters. In the case of, for example, a huge pack of thugs attacking a heroic team, it is permissible for the characters to post some results of combat, to beat down a thug here and there, even though it might appear as a technical violation of Prodigy Rule 1.1. When in doubt, use common sense, and lean toward controlling only your own character, trusting that whoever created the Thugs will post suitable reactions to your attacks. In general, people who recur in a characters storylines or are important to a planned storyline – are considered protected. You should ask permission from their owner before killing them, as that person might become justifiably angry.