After the war anyone that was proven to be in some way responsible for mass murder in the death camps was put on trial, some were hung, some were imprisoned.

Some (along with other Nazi's) escaped and were hunted for decades by groups who sought justice for those murdered. Probably the most prolific was Simon Wiesenthal, a holocaust survivor.

Just last week 94 Oskar Groening, a 94 year old ex SS soldier was sentenced to four years imprisonment for his part in mass murders at Auschwitz. He was a medical orderly and whilst did not actually murder anyone himself was deemed an accessory to the killing of inmates. Groening admitted to being "morally guilty" but denied criminal responsibility. His conviction is likely to be one of the last convictions of its type, simply because with the end of the war being 70 years ago many people of that generation have passed away.

To be blunt about the German peoples' punishment for the death camps: there were not any significant repercussions other than the ordeal of occupation by a foreign power. Historian Tony Judt mentioned in Postwar that some Allied generals pressed into service some German civilians to exhume and properly rebury the deceased victims of the death camps. In other narratives the inhabitants of town and villages were marched through the camps and view the liberated survivors. There were also denazification programs through Germany, particularly in Nazi strongholds like Bavaria and Munich. The effectiveness has been debated because life itself in postwar Germany was a struggle. People had to worry about fulfilling their own basic needs to find shelter and food. They might shuffle through the camp, but never actually acknowledge the war crimes that taken place down the road. The trials at Nuremberg aside (which was not widely broadcasted in Germany) the Western allies were more concerned about bringing reintegrating their portion of Germany politically and economically in preparation for the Cold War. Overall, only a small number of the German high command and those personnel who worked in the concentration camps were executed for war crimes. A slightly larger amount of were sentenced to life in prison, but the sentences were later reduced or commuted.

[As for the reprisals against the Germans for being on the side that attacked Russia, YES.] (https://en.wikipedia.org/wiki/Rape_during_the_occupation_of_Germany) However, take note that the Western allies were not always benevolent conquerors and liberators.

I think your question was in reference to German civilians, but just in case there were instances of Allied troops executing SS prison guards. Probably the most well known incident took place at Dachau in 1945. Although IIRC, it was censored, despite Eisenhower's outrage at vigilante justice. There was an investigation but real disciplinary action was never taken.