WOJ is the Venatori and The Archies purpose is to wipe the memory of particularly dark Demons and Gods. Ones that were defeated by Good Gods. Basically Cthulhu Gods and Demons. When enough of humanity has forgotten the name and purpose of Dark Gods, The Archive exiles them to the Outside. Thats where they become Outsiders.

Once you know that you understand how the Lords of Outer Night and the Fomor (an alliance of dark gods) are everybodies enemies.

Honestly the thing I'm most confused about is that Harry doesn't consider Vadderung/Kringle a friend. They've fought alongside each other in atleast 2 battles. He's given good advice, crucial on separate occasions. Plus he seems like a genuinely fun guy,

19 pages out of 600 word short story. You nerds.

I mean one of the most confusing Fae plots there is in the books- which is saying something- is Mab and Titania opposing each other while the Denarians are running around in Small Favour. The Book also has direct Archangel power confirmation that Lucifer himself was acting in alliance with the Denarians. So there is atleast one significant occaision Mab and Lucifer. Fae and Hell. Working together.

Sex with the Winter/Summer Knight of there respective courts. Mab says what the Mantle will do to defend itself. Winter Knight is part of the Winter Mantle as extensively talked about in Cold Days. Mantle can't defend against itself, would probably indulge in it.

Could be part of Winters purpose is to guard the borders of Hell as well as the Outer Gates.

In some mythologies The Wild Hunt is referred to as the Hounds of Hell. The purpose of the Wild Hunt was to hunt escaped demons and souls from hell. Some of the leaders of the Wild Hunt are said to be notorious figures sent to hell. There was atleast One dodgy Scottish lawyer. Might be some sort of exchange is necessary. At the very least etiquette on whose jurisdiction it is.

Halloween as we know is a confluence, when the barrier is thinner. Traditionally people are more easy to contact spirits and souls from the other side. This would probably include those from Hell, if the amount of serial killer ghosts in pop culture are true.

but begs the question of who introduced them?

I presume the OG Venatori.or said Elder Gods who fought against the Greater Demons. Most of the old said Myths have the Gods commanding some supernatural race or another, against said Gods.

Well from what we learned of Luccio's short story. Thule Society attracts and trains sorcerers turning them into Warlocks. That is they are the anti-wardens, but as Bob said mostly destructive, violent, black magic. It also explains how Kemmler's apprentices were once in all probability relatively minor talents until they started eating ghosts and souls to give themselves power boosts.