Hallo there,
I’d need a bit of advice for my campaign’s next steps and I’m sure you can help me, like you always do.
Forgive the long post: for a quicker reading, all my questions are at section 3.

1 - Introduction

In yesterday’s session, my group had to go down into Nova Castilla’s underhive: when they met a crossroads, they chose to neglect the «right path» markings they found and took willingly the «wrong» way, «just to see what’s there».
Despite the constant whispers, quick shadows and light steps their characters heard or saw, my players were determined to ignore these repeated warning signals, entered an endless dark alley and then wanted to reach the ruins of a tall dome they saw farther on.
The session ended with them at the foot of the dome’s stairs.

Fine enough, both I and they are having a lot of fun with this detour and I’m more than glad to indulge their thirst for adventure. Nonetheless, as they ignored every warning I gave them, I think it is the right time to introduce the Space Skavens I kept for emergencies: bringing in hysteric and psychotic biped rodents who talk in short, high-pitched, over-the-top sentences like «kill, kill, kill», «die human thing/human slave», «humans tastier than sunflower seeds» helps to play down the atmosphere and prevents players from taking things (and/or themselves) too seriously, which is the way we like to play.

Moreover, this could as well open a new scenario for me, allowing me to combine a couple of dead threads I put aside: yet, as stated above, I’d need a bit of advice.

2 - Setting (what the group is doing and will be doing)

The acolytes have been tasked with securing Nova Castilla’s Library of Knowing to the Inquisition, it doesn’t matter how. They chose to ally with a noble family and this will lead them to uncover the Beast House’s network on the planet (they’re still unaware of this): the head of Fenksworld’s Beast Houses is the planetary governor, a renown hunter himself, who (and whose family) at the end will be «dismissed». This way the allied family will be given the governorship and, as arranged in exchange for their promotion, they will hand over the Library to the Inquisition.

Yet Nova Castilla and Fenksworld have an ongoing problem: the Pilgrims of Hayte, who are from time to time blowing up bombs in the hive. Six years ago they managed to make a whole hive collapse (there’s no official explanation yet for that downfall) and now they are trying to do the same with Nova Castilla: nobody knows they exist on the planet, let alone they’re the bombers and the culprits of the hive’s collapse.

So, I was desperately looking for a better hook to introduce them than the usual «the inquisitor orders you to investigate about the Pilgrims of Hayte» and I think the Skaven could be the missing link: in fact, should they cooperate with the Pilgrims of Hayte, this could be the chance to join the ends I was looking for. By the way, they’d be the ideal bombers, for they can move in the smaller passages without being noticed.

Therefore, this detour could allow me to have my players facing the Skaven (just a handful of them) for the first time: when they’ll have dealed with them, under the dome the players will find one of their arsenals, filled with bomb components, and start getting the clues that, over the next adventures, should then get them to the Pilgrims.

3 - Questions

Yet, as I wrote above, I’m unsure about a handful of things: of course I can arrange everything as I want, nevertheless I’d wish there is as much likelihood and accuracy to the setting as possibile.
So, here are the doubts I have at the moment:

3.1 - In your opinion, could the Skaven cooperate with the Pilgrims of Hayte?

3.2 - What would induce them to cooperate with the Pilgrims? The mere hate for the lesser race mankind is?

3.3 - In the fantasy setting, the Skaven god is the Horned rat: are there similarities between him and any of the Chaos gods? Too bad reading the Lexicanum wasn’t helpful on this matter.

3.4 - What could a suitable Chaos god for the Skaven be? I was used to think they were somehow tied to Nurgle, yet by reading the Lexicanum I had to change my mind.

3.5 - As I got it, the Pilgrims are better served «Chaos undivided»: but what is the ideal gods’ ranking among them? Surely Khorne comes first, followed ex aequo by Tzeentch and Slaanesh: far, far away comes Nurgle, almost shunned. Am I right?

Thank you in advance for whatever piece of advice you’ll be giving!

Skaven following a chaos god? well thats an odd idea. Skaven are more of the back stabing idiots who dont even know what a god is. Or they could have their own patheon of gods like how the orks have gork and mork. Now onto your qquestions. I dont belive they would work wit the pilgrim unless the pilgrims had something they really wanted.

We explored the 'Rats In Space' theme in one of our little campaigns, and it went quite well. The only thing we did to avoid mixing up two different settings (WHFB & WH40k) was to make the rats mutants instead of xenos.

This also allowed us to answer any questions like 'why these rats would consort with the minions of Chaos'

Being the bastard progeny of the Great Unclean One called The Saviour, the ratmen first appeared in the lower decks of Port Wrath (if memory serves) and later spread across the Calixis sector worlds thanks to ineptitude of our fearless Inquisitors, who were invariably too busy (running from daemons) to spend some time to eliminate the furry mutants.

Back to the original question, the Pilgrims could just as well despise the ratmen, but at the same time they could work together, either united by some common goal or controlled by some greater being (or both, as is often the case). For example, you could turn ratmen into mutants, maybe making them the degenerate and corrupted descendants of once-proud community of ratlings. They could strive to overthrow human government of the planet to "restore ratlings' rightful place as masters of this world" or something like that. To this end they could strike a deal with the Pilgims, who couldn't care less for ratmens' crazy ideals, but will work with them because they need a secure base of operations while they're scheming to raise hell on the planet. The Pilgrims - in turn (unknown to them, maybe) - could work for a Chaos Sorcerer obsessed with unearthing a profane artifact long lost somewhere beneath the ratmens' warrens, who is just using both Pilgrims and ratmen to draw unwanted attention away from his own person.

True Skaven are not too stupid to grasp the tenet of religion, especially not when these are reinforced with fear. The Horned Rate anyone?

The Pilgrims of Hayte are well known for summoning daemons. Maybe they conjured up The Horned Rat to help them destroy Fenksworld, and he/it created the "skaven" (by warping giant Underhive rats) for just that purpose? Of course, in classic Frankenstein fashion, the creations could decide to turn against their "masters"...

Thank you all for your replies, you gave me good hints that now I only need to develop further.

As for the Skaven origin, I’m still swinging between them being mutant creatures (à la Teenage Mutant Ninja Turtles: rats transformed by exposition to pollution and warpstones) or vermin coming from the outside, very apt to adapt themselves to any environment (as a proper vermin should do).

Anyhow, now I’m quite sure the Skaven/ratmen and the Pilgrims can work together, at least until one’s goals get along with the other’s, obviously with some backstabbing involved: I can see the Skaven as the «bringers of woe», the ones physically placing the bombs, while the Pilgrims plot and get stronger. The Skaven agreed to help them in exchange for a better knowledge of the Warp and the warpstones, which the Pilgrims can produce by trapping lesser demons in stones or crystals.

A bit cheesy perhaps but it can work: it has that «science fiction movies of the 50s» (and perhaps even a «fantasy B-movies of the early 80s») flavour I enjoy.

There is actually a xenos race that has often been called the 'space skaven' or 'the skaven of 40K' and that is the Hrud. You will not find much official information about them, only some vague hints (such as Space Marines cleansing Hrud warrens), but in the book Xenology they are detailed more elaborately.

Most sources mention they are swathed in cloaks and bandages, emit a foul smell, and live between the decks of the giant spacecraft or in the lightless recesses of hive cities. They are either dimension walkers or else their mere presence is poisonous to the proper passing of time. They possess some terrifying weapons what use extradimensional matter or something, which are detailed in Disciples of the Dark Gods under the Cold Trade in xenos artefacts.