at least if you are at his unnatural sense range?, basically he's not seeing.

Arguably, but it would depend on context. I think it would be uncontroversial to say that they are immune to the effects of stummers and chameleon cloaks.

I would say they are probably immune to the stealth of someone simply hiding in the shadows, but if it was for example someone tailing the Astropath in a crowd then stealth would work as normal.

I don't think that creatures with the Unnatural Senses trait are automatically aware of everything going on within the range. They are just allowed to make an Awareness test (and maybe do not get negative modifiers because of things like shadows and so on) even if there are obstacles between them and the target which would normally prohibit Awareness tests. The creature may have an unnatural sense with which to perceive their surroundings but they still have to focus their attention to specific points within the range in order to notice someone approaching.

For example I have a psyker with the Warp Perception power in my group. When he uses it he is not automatically aware of everything within range. He can "just" quickly shift his incorporeal soul (or whatever) within range and so see around corners, through walls or in pockets and under coats. To notice anything important he still has to take an Awareness test. Luckily for him, this psyker has also the Seeker role ...

It would really depend on the source of the 'Unnatural Senses'. For an Astropath who is basically using his Witch-Sight, he'd be able to see the spiritual aura of the living in the area. Don't see how a Chameleoline would help against that. Likewise, I think animals with heightened senses would be able to detect pheromones and scents, etc, on a level that would make visual based stealth techniques obsolete.

Exactly so.

Taking the example of an astropath, darkness would be no protection so there'd be no penalty for it. You'd still have to make an awareness check vs stealth for other reasons - as noted, a good example is someone trying to pick his pocket whilst he's bustling through a crowd.

Aware of the existence of everyone within unnatural senses range? Yes, peripherally.

Concentrating on what every single one of them is doing simultaneously? No.

Noticing that that specific individual just lifted your inquisitorial rosette? Maybe, maybe not. Best make an awareness test.

My group has an on going argument that the astropath's unnatural senses should go though walls. I shut it down for game balance reasons but is there a lore answer I can give them to just shut them up?

The Astropath player is arguing that since the Unnat. senses are psychic in nature it would go though physical objects, same idea Cogniczar is saying about the Cloak but applied to walls.

Do the rules for Unnatural Senses does it say characters with the Trait are immune to stealth?

I also would think that within range physical objects (like walls) should not hinder Warp Perception in any way. The psyker just lets his perception float through the wall. Otherwise Warp Perception would be rather weak I'd say. But again, the psyker does not automatically see what's going on behind said wall, he has to succeed on an Awareness test as usual to do so.

I allow Unnatural Senses to extend though solid objects, but I require an Awareness roll to pick up anything that couldn't be picked up with normal senses.

But the thing is: if the players are walking through an abandoned under hive, someone try to catch them by surprise walking from cover to cover using stealth. Wouldnt the astropath be able to just feel him through his unnatural sense??

They don't suffer penalties from Darkness since it only applies to vision, and so on.

But the thing is: if the players are walking through an abandoned under hive, someone try to catch them by surprise walking from cover to cover using stealth. Wouldnt the astropath be able to just feel him through his unnatural sense??

He might. I would check with an opposed Awareness vs Stealth test. No negative modifiers because of darkness and so on for the Awareness and probably a negative modifier for Stealth, because the usual techniques to hide from sight do not work.

Edit:

And if it's not critical for the story then let the astropath just feel the stalker. Remember: Only roll tests if the outcome is important for the story.