*- He's human! Sort of. Kind of. Not entirely. See, when he was little he got repeatedly killed and revived for the purpose of kicking him across the incarnational cycle so he'd bring all that power back with him, and they succeeded! This means that, if you're able to pick up on whether someone is human or not he ... probably feels funny most of the time.
This is probably aggravated by the fact that, of the Six Paths, he's NEVER in the Path of Humans. The Path of Humans ends up expressing his nature this-life, which basically means taking that whole "living weapon" thing, shaking it up, amping it to 11, and taking the safeties and controls off. Lucky for everyone he hates it.
Which's why he's never in it, so he's usually probably leaking bits of Something Else overlaid on 'human'. Most of the time, he settles in the Path of Heaven; if he's in a fight or threat situation, he'll usually go Path of Hell. Yep, his two most common Paths are the most seemingly contradictory, and he's usually going to read like he's a bit "tainted" either divine or demonic.
*- For empaths/telepaths, he DOES shield, and his mind is pretty guarded. This is probably a good thing, since his mind is ... off-kilter. What he does allow to leak is basically "big predator", very prickly, and not really "normal human psyche"; it's probably pretty easy to tell you're not dealing with someone who was raised normal human wormbaby.
If you get past the shields, it might be heavily situational and heavily booby-trapped. He's not sensitive in the normal sense, but he is good enough to notice if someone's past his defenses and rooting around, and he's perfectly happy to turn any invasion into an invitation to first-hand experience of one of his worse memories, with a little added power to make sure it feels extra vivid and real. Given how fussily private he is, it'd take damn special circumstances to NOT get him being gleefully unpleasant about this.
That being said, I -WILL- try to include in tags anything that might be relevant/leaking with Sensitive characters.
*- Depending on how your abilities work, you will either have an easier time with the Path of Hell illusions, or harder.
If you have a way to sense that it's "not real" that isn't affected by picking up on HIM, you can probably fend off a lot of the basic stuff unless he's really pouring power into it or using the Vongola Gear to amplify it. Sensing energy or seeing magic would work, since it'd read as whatever-the-illusion-is over a framework of a sort of energy-construct, and anything "living" in an illusion won't have it's own aura/mind, but rather a construct-framework made of his energy.
The bad news is that it basically works by hijacking your perceptions and then using that as leverage to make the illusions real, and the Mist Flame allows him to add real weight to it; for extra fun, most of those things he's throwing are things he has actual firsthand knowledge of, and therefore is basically broadcasting and sharing from real experience. Since it's the will of the illusionist that makes it real, if your talent is such that you're picking up on him mentally, it might end up working AGAINST you, in that he's got enough power and force of will that as far as he's concerned, it's real for as long as he says it's real.
*- On that note, if you have something that allows you to see through illusions, he has some ambient illusions that're continually in effect; currently he's both covering scars and covering that he's kind of walking dead/skin and bones, recovering from several months in a stasis tank and getting the shit kicked out of his body. With his normal sleeves/gloves/etc., the only visible scar that's illusion-covered is a too-regular surgical-scar circle around his red eye that's pretty faded, but visible; there's also a lot of very visible punctures/lines/similarly "that's way too regular to be a combat injury/accidental injury" scars up and down his arms, as well as a few on his back/chest. There's also, for a while yet, some bandages over healing injuries.
*-The Vongola Gear/Mist Earring has a mind of its own...two of them, sort of. One is Mukurou, the Box Weapon, which is an owl that's a sort of familiar spirit. Mukurou seems to be pretty damn calm/chill, and fairly obedient - the owl doesn't have a very strong personality.
The other is pretty beaten down, probably keeping up a lot of "nothing to see here move along" shields, and basically dormant, and it's the surviving piece of Daemon Spade's will. While technically the "Will of the Ring" is a factor, Spade's pretty much run up a white flag and been pounded into the ground like a tent peg enough that if you get past the "nothing to see here" he's willfully semiconscious and in a state of "...ow". Technically speaking it's hard for anyone outside to even access the Will of the Ring besides the sense that the earrings -ARE- "alive", and it'd be easy to mistake Mukurou for whatever's "alive" in there; if you do manage to get access, it'd take a lot of effort and energy to get more than grumpily swatted at to go away. Spade got the CRAP beaten out of him and is basically resting, recovering, and Having a Think.
It would also be hard to poke too much without Mukuro noticing, since he's kind of connected to the Earrings and usually WEARING them, and he will probably strongly discourage too much poking, possibly with violence. The easiest way to do it would be to get them away from him somehow, and that'd be a task in and of itself.
Oh, and the trick where the owl turns into a staff/weapon? It would be noticeable to any psychics that the weapon is alive and is the owl, if they didn't see it transform to know that to begin with.