[ OOC ] : These are old questions I never got around to answering on main when I first posted Specchio's sheet, so let's take a look!
Hemispheres is a rather versatile stand, so it can be a little confusing! Most of its abilities center around reflection, and I try not to overdo it in terms of how much it can do. My main idea behind Hemispheres is that it would be a sort of jack-of-all-trades, and more of a "support" stand since a majority of Team Bucciarati is more on the offensive side in regards to their abilities. (To me, Moody Blues and Gold Experience are the more "supportive" there... but even then, GE could still pack a punch - especially with the retconned ability vs. Bucciarati!)
To help with a quick overview, let's narrow down Hemispheres abilities to these four: Reflexive, Disorientation (CQC), Reflective (Ranged), Absorption (Healing).
Full explanation of each under the cut! Always happy to answer more questions, and that ask box is open! :]
Reflexive
Hemispheres was an untamed stand when it first manifested to Specchio. While not as dangerous as Purple Haze, it still made growing up a stand user who was unaware of their own abilities very difficult. Consider Hemispheres' reflexive ability to be like an unconscious aura surrounding Specchio - a radius that only effects non-stand users and drives them away subconsciously. It's basically the "bad vibes" circle. Hemispheres did this as a way of protecting Specchio since he was a bit of a loner and anxious around strangers, but this ended up adding on to the issue because it made it very difficult to socialize. While stand users can perceive this aura, they usually have the fortitude to pass by it completely. I suppose if a non-stand user was very bold, they could bypass it as well... but, well, Specchio was never so lucky to have that happen.
As Specchio honed his talents under Bucciarati's training, he was able to deactivate this ability - like a switch... though, this may have also come with him learning to be more comfortable around people. The only times it ever really shows through is if he's especially fearful, but it no longer holds the same power it once did.
I suppose you can consider this ability defunct.
Disorientation (CQC)
Hemispheres is especially weak in close-quarters, even though that's the limit of it's physical range. It isn't a punch stand, nor is it extremely durable, being perhaps only a little more well-off than Specchio is (given it isn't, well, fleshy). However, there is one ability that Hemispheres can only activate via contact: disorientation. With a quick swipe of it's palm, Hemispheres will touch an adversary and activate this ability, which will only last within a certain range of Specchio. The adversary will have the hemispheres of their brain swap, switching lefts and rights, ups and downs... in layman's terms, consider this similar to a game mechanic that swaps your control scheme.
One who is especially in-tune to their surroundings and body may be able to overcome the effects of this disorienting swap, but it can be especially bad for those who have to worry about verticality as well, such as vs. Secco when he dives beneath the ground.
Reflective (Ranged)
This could be considered Hemispheres' main ability. While not offensive, it relies on trickery to aid Specchio or his allies in a fight. 1-2 reflective panes can be summoned within a formidable range of Specchio (basically, so long as he can see it at the time of creation). These panes have no border, and sort of blend in with its surroundings to be indiscernible as its own shape until you're right up against it. They take around 2-3 hits to break, but will crack with just one. The shape of it can also be altered, but this requires significant focus from Specchio to keep maintained, lest the illusion warp and become more easy to discover (such as in his vs. Formaggio fight with Narancia, when he turned the mirror somewhat concave in order to create a mirror-magnetizing effect to fool Formaggio).
Specchio usually uses these in order to make a getaway by concealing himself, or to buy time by making a barrier between him and the enemy. It's also worth noting that these mirrors are one-way, meaning that Specchio or an ally could see through them from the other side.
Absorption (Healing)
Now, this is an ability I actually never got to use in Filo Aureo (Specchio's AU)! I never really used it because I wondered if it would be too much, but I think it might have it's place in the right scenario, so I still keep it around. It's hinted at in Specchio's backstory with how he survived his house fire, with his burn wounds being halved and reflected across his body - which while this lead to more scar tissue, prevented him from losing his left arm entirely. In short, Specchio can reflect wounds across the median of his body, OR reflect wounds from someone else's body to his own. I believe this fits in with his self-sacrificial mentality... and could also probably lead to some angsty situations of trying to convince him not to take a wound for you.
This ability could be considered more theoretical in a sense, since he never really utilized it in his "canon".