In a word? Spirits. The ability to call on them, make them do stuff, and even sense them. We can sense people's 'spirit' as a form of sensing. There's also the extra control over our emotions that we are afforded by our training.
The spirits themselves can do all sorts of stuff. They can be used by their lonesome, infused into stuff, even infused into ourselves. So there's a lot of variety there.
Oh, yeah, and we have a little spirit companion. So there's that.
You've captured the essence of it. Now I'll build on it. So we call these spirits Genki. They aren't really souls in the traditional sense of the word. They've always been Genki. They were never human souls or anything like that. As far as we know the Genki have always lived parallel to us in their Pure World while we remained in our Impure World. Its through the ritualistic teachings of House Katsuryoku that we form a contract with these beings and bend them to our will. Outside of that they simply exist alongside us. This is perhaps one of the most fantastic parts about the clan because these spirits can be
anything. There is near limitless potential for Genki limited perhaps only by one's own imagination. Genki can come in all shapes and sizes. In terms of strength there is sort of two unspoken distinctions between Genki. Generic Genki, which only require chakra to summon and control, or unique Genki. These unique Genki are what one would think of legendary spirits, named spirits, and such. These Genki have unique abilities and require not only a sacrifice of a large amount of chakra but also occasionally blood.
Now, the training you underwent in the old thread involved honing your convictions and then undergoing a ritual which made you aware of Genki. So calling back basic chakra training we learn that chakra is composed of Spiritual and Physical energies - the Yin and Yang. As the clan suggests it is heavily based on the Spiritual aspect of things. Genki themselves are composed of and use Ethereal Energy to interact with our Impure World. Ethereal Energy is simply to purest form of Spiritual Energy. So the way one comes to harness their Spiritual Energy is by honing convictions. Which is rather difficult to do which is why most people simply resign themselves to a strict physical training regimen and harness their Physical Energy instead.
So to do this you spent quite some time meditating with Amaimon and your fellow Openings (the first rank in the clan). The result of this training and meditation was full control over your emotions and convictions. In terms of abilities this is the first basic ability of the clan. You gain absolute mastery over your emotions. So what does mastery actually mean? We don't simply become cold killing machines with no emotions. Mastery implies the ability to not only void our emotions but also feel them at our own volition. This is exactly that - I can feel normal emotions at my character's choice. I can also feel no emotion. I can feel only hate. Or only love. This offers limitless options on emotions we can feel...or not feel. And emotion is also highly connected to chakra as implied in the canon story. So it does allow for some customs room as well, should one go down that path eventually. Now this means we become resistant to things like Killing Intent as well. Anything that attempts to exploit our emotions we can resist with ease. Now this doesn't mean much for Killing Intent with you. You're an official sage and such so no one can really come at you with Killing Intent. But there could be some customs out there that I'm not aware of that could still exploit emotions regardless of rank.
So the second ability to gain once the blood ritual is complete is the awakening of your awareness. The awareness does not extent to souls and Genki alone. It involves anything closely connected to Spiritual Energy. So souls of living humans is included in that. We can sense life essentially. But this also means we cannot sense the dead. So for example, the Six Paths of Pein we can't sense because they are simply corpses controlled by chakra. We can sense Edo Tenseis because the captured souls of their victims are within the bodies. We can sense Genki as well. We can also see Genki, if I may add. We cannot sense chakra, however. Chakra is the impure combination of Physical and Spiritual Energy. Thus we cannot sense it.
We'll cover infusions soon.
Questions?