Yes, you're correct that the device you're referring to is the Genickschussanlage. They existed in a few camps, but the most famous one is at Buchenwald, where both Soviet POWs and others were executed; I'm not sure if that was the first one but if you look up "Genickschussanlage" it's what you're going to find the most information about. I've actually been there and stood next to it. It's pretty creepy, as you might imagine.

So, to get to your questions:

1. "Sanctioned by the higher-ups" may be an odd question to ask about things that occurred in concentration camps. It's worth remembering that many of the killing methods used in the camps were improvised or evolved over time from practices elsewhere in the system (e.g. the gassing methods used in the extermination camps originated with the murder of disabled people during Operation T4). I'm not aware of any specific written approval from above for the Genickschussanlage in particular (if someone does know then feel free to correct me, because I'd be really interested to see the document), but the executions of Soviet POWs were authorized by an order known as the "Commissar Order", which was issued prior to the start of Operation Barbarossa (which you can read a translation of here if you're curious).
2. There wasn't any secrecy in terms of "covering up" what happened to the prisoners themselves; most of the prisoners shot in the Genickschussanlage were executed right away and there was no documentation. The only secrecy was keeping the prisoners from knowing what was going to happen to them until they were killed (in this case by making them think they were being measured). This is similar to the more well-known deception methods used at the extermination camps (fake train time tables, SS officers dressed as doctors, "showers", etc.).
3. They weren't "special" in the sense that this execution method was chosen for a specific type of prisoner, no. The Soviet POWs who were executed in this way generally fell into the same categories of Soviet prisoners who were executed elsewhere: political commissars, communist party members, Jews, and others the Germans considered "undesirable" (the term they used was unträgbare Elemente). In the POW camps at or near the front (usually transit camps) or in the occupied territories, these prisoners would just be taken out of the camp and shot by the Sicherheitsdienst or regular soldiers. For the prisoners of war who were brought back to Germany before being "sorted" (the German term for this was Aussonderung, or "weeding out"), those who were identified as "undesirable" were sent to a nearby concentration camp (e.g., Buchenwald, Sachsenhausen) for execution.

I'm really excited that someone is interested in Soviet prisoners. This is what I work on in my day job and I really hate that people will often learn so much about the Holocaust and have no idea about what happened to Soviet POWs. I can suggest reading on Soviet POWs more generally if you'd like, but if you want to read about Soviet POWs in concentration camps in particular, it's discussed in the diary of a Sachsenhausen political prisoner named Emil Büge (which was published as 1470 KZ-Geheimnisse). He witnessed the arrival of transports of Soviet prisoners from one of the camps near there (I can't remember which and I really ought to be able to) who were later executed (although I think they were just shot by a firing squad). This is probably more detail than you wanted but like I said I'm just excited that someone is interested in this. I'd be happy to answer more questions about this or provide more sources.