In Warhammer 40k the Imperium governments are responsible for giving their psyker to the Black Ship or the Inquisition, so it's mainly up to you. ;)
Each world will have it's own method. Don't forget that an untrained Psyker is far more dangerous than a trained one (even a Chaosian one); just look at the psychic phenomena table, or the next one: perils of the warp, it goes to just have some temperature drop to mass demon possession, with some funny thing like blood rain from all ceiling ;)
As long as your Psyker doesn't use his power, it'll will be very very unlikely that he will be found. Psykers are rare, and the ones with warp sense (Psyniscience test for free action) even rarer (except for the player, they always take warp sense ;) )
You can also have checkpoint at the spaceport, or before entering some sensible zones; these checkpoints may have a Psyker checking the visitors. But don't forget that they generally have better uses, if you have Psykers at checkpoint it must be very important.
But if your party does something out of the ordinary, something noticeable by a human, like all the food going sour around the Psyker, an inversion of gravity, someone hit by something invisible, or the roulette in the casino giving always the same winner, the chance that the populace are fleeing the zone screaming 'Psyker' is high.
And if there is reasonable suspicion of a Psyker being somewhere, the Inquisition will be there, and that is a risk.
Also, your group is not the only one trying to undermine the Imperium, so an Inquisitor may be there coincidentally. (The inquisition group may also be there for à false alert, and digging some heretic stuff.)
They have never been on "Good" Terms
Chaos and the Emperor have always been at-odds, however, what the exact story is tends to vary.
The most generally-accepted origin story, and by that I mean the one most-often referenced by the community and by GW itself, is the story of the Shamans, sourced from Realm of Chaos: Lost and the Damned (1990).
Realm of Chaos: The Lost and the Damned
In this version, the Emperor is the combination of the souls of a group of human Mystics called Shamans. The Shamans guided humanity, but, as the influence of the Warp grew (note that the Chaos Gods themselves were still dormant at this time), they found that they were dying-out, and their reincarnation abilities were beginning to deteriorate due to Warp Predation. Recognizing Mankind's need for guidance, they took poison and "died as one", which allowed their souls to collect and reincarnate all at the same time, and escape the predatory spirits of the Warp.
(p. 174-175)
At first, the Emperor tried to simply "guide" Humanity, manipulating it from behind-the scenes to avoid the paths of Chaos. However, as he did this, the Chaos Gods became more and more aware of his actions and began to wake. Each God opposed the Emperor:
- Khorne woke first, and several wars erupted across Terra to Herald his awakening
- Tzneetch would wake next, after which political intrigue and schemes would come to light and cause huge strife
- Nurgle would awaken next, and a huge plague spread across the planet
All of these are predicted (but not entirely sourced) to have occurred within the 40K Terra's "Medieval" Period but have extended up until the Unification Wars, the conclusion of which decreased the influence of the Ruinous Powers in humanity by unifying Humans into one purpose: the Great Crusade, after which Horus betrays the Emperor and 40K history is born.
However, it wouldn't be 40K if there wasn't another story that casts doubt on the canonicity of the Shamans...
Vengeful Spirit (2014)
This is the story that you have heard referenced in the comments on the question. In Vengeful Spirit, the Emperor and Alivia Sureka travel to Molech and enter a Gateway to the Realm of Chaos. Here, the Emperor makes a pact with the Chaos Gods where he gets power in return for spreading Chaos worship throughout Humanity, but immediately reneges on his end of the bargain and becomes the Anathema.
Of course, this has some inherent flaws:
- Anything going into the Warp has to have a Gellar Field Generator (or the favor of the Chaos Gods) to stand a chance of making it out without annihilating. Now, the Emperor may have been able to do this after the bargain was made simply on account of his psychic strength, and it is possible that the Chaos Gods allowed him access to their sanctum, but it is not very feasible that Alivia Sureka, even a Perpetual as she was, would have been able to survive this.
- This tale also implies that the three Chaos Gods were already awake before the Emperor became the Emperor, and thus should have had no problem running-over Humanity without the need for a bargain with the Emperor.
- For beings known to be able to see the future, this seems remarkably short-sighted. This, in-particular, questions the purpose of Tzeentch, because how can a god of intrigue and plans ever hope to succeed if he is incapable of seeing such a short distance into the future. Of course, this may have been, as /tg/ would say, "Just as Planned," but considering the amount of hassle the Emperor has been to Tzeentch, this again seems unlikely.
- It still doesn't explain the "origins" of the Emperor. It talks about something the Emperor did, but does nothing to explain how he got to be The Emperor in the fist place.
Either Way, The Emperor and Chaos have never gotten along
Best Answer
Ogryns being able to lead squads of their own kind is the result of the Biochemical Ogryn Neural Enhancement treatment, or the BONE treatment. This makes them more intelligent and capable enough to serve as sergeants called Bone'eads. Ogryns that seem to be smart enough for this are tested and, if they come out as positive, undergo this treatment. Exactly how much smarter they become is unclear.
As for their acceptance, Ogryns are not very smart but very loyal, will follow orders to the letter and have an unshakable faith in the Emperor, seeing all orders given to them as having come from His Imperial Majesty himself. Furthermore, they are very strong, carry big guns (or other weapons) and can rip enemies in half with their bare hands, making them very useful on the battlefield.
Not all elements within the Imperium like them, because they are abhumans. For example, the Monodominant faction within the Inquisition wants to exterminate all beings who are not pure humans, like Abhumans, mutants, Psykers, Navigators, Astropaths and Space Marines. But for the time being the contributions of the Ogryns seem to outweight the naysayers, and as such they remain under arms.