Not far from the Halo Stars, is not a very exact location. Nor is a mining operation a governmental type. You might substitute the leader of the operations or the Administratum contact that reports for the tithes as a "governor".

There's going to be some Adpetus presence, at least Administratum because they need to keep the tithes running, Based on the material they are extracting the Astra Telepathica might have a hold there as well to make sure the colony remains in contact since the resource is so useful to them. You mention both the Ecclesiarchy and the Mechanicus as well being important. Mechanicus very much so since they have to maintain the colony.

Do they not have PDF forces to help keep things in line? A local militia? Some form of security in any way shape or form?

Interesting traditions.

In your 4 main areas you only list 3 main areas.

I mean, you can just say that they suppress psychic powers, that's not unbelievable. As such the general population would likely have a very low number of psykers born among the population.

See you mention a governing body yourself "The Overseers" And Slaugth have weird names anyways that mean nothing like Master Nonesuch or Miss Book. Just come up with Overseer (Insert throwaway name) for the head overseer.

Why keep the existence of their bosses a secret?

Now come to think of it look into the Amaranthyne (I think that's the spelling) Syndicate from Disciples of the Dark Gods. They work heavily with the Slaught and are a good human face for them so we don't have these issues.

So they cover up the existence of their Overseers, but their Overseers decide the laws of the place the people are supposed to follow?

The Laws:

1. Note the fact that these properties of the ore need to be determined. If they say suppress psyker powers it's likely the gene would get repressed in the population. But there would be rare ones certainly. What do the Slaught want with them?

The rest make sense, that's actually pretty common probably.

Why would the Inquisitor personally be worried about this? Why not have some group contact the inquisitor, and then have the cell investigate it. Small thing but an Ordo Xenos inquisitor won't really care, heck even some Hereticus wouldnt' depending on their specialty.

Woah Woah WOAH, What if the acolytes inquisitor isn't one for blowing up a valuable deposit of the rare and useful mineral just because some smucks they threw at the problem died trying to figure it out? Remember stuff like this is an escalation sort of deal. You send a team of expendable acolytes, and if they die you send in throne agents, if they die you get something more powerful and deal with it yourself, and if that doesn't work you get out and THEN blow it up.

Ok, but you need to describe what the normal workers actually have to show that the apartment is better.

What if they don't find the box?

Ok, but...if the woman will look for them anyways then why even bother with the box? It needs to have something extra for them to discover if you're just going to have the woman find them anyways.

What stops them from being both overt and quick? You should probably map this timeline out based on them getting degrees of Success for the box discovery if you want the woman dead.

So what are the enforcer's order here? Kill the woman or not? What about the acolytes finding them interferes with this, and why is the toddler so important for them not to just kill it?

A psyker baby is a dangerous thing, and they'd need to put it away somewhere before it hurts everyone around them.

Ok, but how are the acolytes supposed to discover any of this if the woman is dead?

Why can't the acolytes fight/hold them off you yourself said there were rebellious elements within the colony. Even then you said the forces aligned to the Slaugh were few but faithful in number.

I mean if you wanted some silly binary you might have actually just spelled out Omega in binary: 01001111 01101101 01100101 01100111 01100001

How are they supposed to find out about the Magos at all?

Well this is a dang geographical anomaly, all vents lead to a single hangar?!

Why not have a broken down vehicle they might fix with the Magos' or tech priest's help?

You seem to have left out an ending and aftermath of a final confrontation.

Overall some good notes to run a game with, but some minor things to think about and modify. Well that and you need to have a goal in mind. Are the acolytes supposed to just leave or something if they find the true nature of the Overseers? I mean the Rogue Trader might have the idea to bombard the area but that'd lose a valuable resource. What were the psykers being harvested for? What's the Overseer's goals with the ore? Lot of unanswered questions here.

Thank you for the indepth reply! I will be looking into your suggestions, but i dont have much time until sunday evening. As for the location: i did not feel it was very important to have a specific location, and left it intentionally vague so that other GMs can do what they wish with it

I get that, but if you're offering up an adventure for use details like that become important. You're putting work on the "customer" at that point. Which lowers the chance they'll use it.

Even the published adventures state where the location is, and most fan made adventures use locations that already exist in the Calaxis sector (or askellon but it's pretty obvious this is a 1E adventure).