Who kills prisoners?

Answer 1

The person applying the pesticide to kill thousands at a time or starting the diesel engine to create carbon monoxide poisoning were normally SS staff. They were in charge of the camps.

The Jews with "special tasks" (Sonderkommando) worked with leading people to the gas chambers and collecting the bodies afterwards, prolonging their own life with a few months.

In case of execution with arms, it would have been SS soldiers.

As the officers of the regular army protested before the dirty deeds of executing civilians and POWs, SS had to take over the killings, with Einsatzgruppen that ambulated in field to execute collected people that were condemned to perishing according to the racist ideas or because of political opposition.

In the camps, not a few threw themselves against the electrified fences, to terminate the suffering.

Rudolf Höss was in charge of Auschwitz II for the longest time, and he execute the orders from SS chief Heinrich Himmler, elaborated by Reinhard Heydrich as presented in 1942 ("the final solution"). The person ultimately responsible, who Himmler answered to was Adolf Hitler. But, Hitler and his National Socialist party had been voted with majority into power in 1933, with a strong public support in Germany. In most countries there were lots of people regarding Hitler as a role-model, almost a hero, as racism and the antipathy against revolutionary internationalist communism was strong in many countries, which Hitler had subdued with his nationalist Labour party.

Also in all German occupied territories there were many collaborators, who gladly handed over Jews, with or without reward.

So in fact a large part of humankind is responsible for the crime against humanity committed in the genocide during WWII.