As the title suggests. Was the average German/member of public aware of the existence of the concentration camps and what happened within them?
The average German was aware that:
there were concentration camps in Germany which opponents of the regime and Jews were sent to, and later also homosexuals, prostitutes, vagrants, Jehova's witnesses, and convicted criminals. Hitler came to power in January 1933. On February 27 a Dutch communist and recent immigrant to Germany set fire to the Reichstag (parliament) building as a protest against the regime. The nazis seized upon this as a pretext to outlaw the communist party and arrest tens of thousands communists and other left-wing opponents as well as Jews. These were incarcerated in about 100 improvised camps. Later these would be consolidated under the auspices of the SS into a number of large, uniform camps that we are now familiar with, such as Dachau, Buchenwald, Bergen-Belsen, Sachsenhausen, etc.
people were treated badly and died in the concentration camps. This was not a secret, though the usual reasons given to the next of kin and the outside world were disease (true enough), attempts to escape, and suicide.
the dead were burned in crematoria. Most camps were located quite close to villages and towns, and the smell of burning corpses was unmistakable.
from 1941 onwards German Jews and Jews in the occupied territories were being sent “to the East” to a fate not exactly known but certainly largely understood to be possibly death for many of them. Officially they were being “resettled in the East”. However, news of the rounding up of Polish Jews in ghettos from late 1939 on, were they died in large numbers, was widespread ,and many rumors and stories circulated about mass shootings of Soviet Jews by the Einsatzgruppen (special SS units) in the wake of the German invasion of the Soviet Union in June 1941. The deportation of German Jews proceeded entirely in the open, and was in fact heralded as a triumph of nazi policy to make Germany judenfrei (free of Jews) or judenrein (clean of Jews). Town after town was officially declared judenfrei when all of the Jewish inhabitants had been deported.
The average German was not aware that:
This is what the German people meant when they said after the war “wir haben es nich gewusst” (we did not know). They did not know about the gas chambers. They did not know that there were purpose-built death camps that differed from the concentration camps they were familiar with. They did know everything I have listed above and they did know that deportation meant possible death, sooner or later.
All of the above applies to the average German only. Of course there were many who knew more: the SS, the German factories that supplied the early gas vans, the crematoria and the Zyklon-B, the people in charge of processing the gold teeth and human hair that was sent back from the death camps, the railway employees that ran the trains to the death camps, etc. etc.