For the Monster of the Week question, I've never played that system but have a rough idea of the game from its Evil Hat description. If (We Are) Anonymous is having trouble with PCs gunning down the monsters, then consider adding consequence reactions. Let these sorts of societal, police, and other NPC elements help pressure the PCs into taking less extreme measures. Here are 3 examples of what I mean:
1a) Portray the monster as a hiding in plain sight John Doe (wide range of how to make this happen) and have the PCs get caught gunning down the person. This could happen with some passer by seeing it and reporting to the police or getting recorded & posted online, etc. Then it could lead to criminal investigations, social blow back, and so on.
1b) Pretty much the same as #1, but make the hiding in plain sight person have some sort of fame / well known / celebrity status, so that any action taken against the person would cause similar repercussions but ramped up exponentially. E.g. Beyonce has her Beyhive that is more than willing to rain hell down on anyone that so much as slanders her name, so imagine is a group of unknowns tried to harm her.
2) If the PCs are working for a larger group, e.g. the FBI to Agents Fox Mulder and Dana Scully, then have their bosses issue new directives such as capture, not kill. That could open many doors for future game opportunities--what does that group do with the captured monsters, what if the monsters escape, etc.
3) Have other NPC forces act as immediate confounders to the PCs. Here a a few mini examples:
A) The government. Monster creates some dangerous pathogen, so the CDC, National Guard, etc. come in to quarantine the area and have a widespread presence everywhere around, so that it becomes very difficult for the PCs to get enough alone time to gun down the monster. B) For a conspiratorial twist, the incoming group could be something akin to Monarch (King Kong / Godzilla). C) Alternatively, there could be a rival group hunting the monster for their own reasons and have their own tactics. If they team up with the PCs, it could mean adopting different strategies. Or if they don't team up, then many the rival hunters keep appearing at the right place at the right time to botch the PCs shoot 'em up strategy. D) Also, hunters doesn't mean they have to kill either; a fun twist might make them 'savers / conservationists'. The 'hunters saviors' could be members of a monster-friendly version of any well known conservation groups for endangered species (like WWF or PETA). E) Riffing of the previous example, it could also be a supernatural-friendly savior that seeks to intervene, like in Grimm where the main character seeks to keep the peace between humans and other creatures.