These were used in the Prison camps to dispose of the dead bodies and thus hide much of the evidence, making an exact body count a difficult task.
Yes, the crematoria (crematories) were for burning corpses.
The corpses were burned in crematoria.
In the context of the Holocaust, fiery furnaces refers to the crematoria (used to burn the victims' corpses).
"Crematoria" is a noun.
Generally speaking, bodies were not, no, but ashes from those who had been sent to the crematoria were frequently dumped into rivers, yes. The ashes of the defendants hanged at the Nuremberg Trials were also cremated and dumped into a river.
no
The only weapon really used in the Holocaust were Gas chambers using Zyklon-B rodenticide gas, (killing so many the extermination-camp crematoria had to run continually). Before this, many victims were simply shot, but the Nazis realised this was too inefficient for their mass-murder policy, and had bad psychological effects on the soldiers involved.
A furnace or establishment for burning (cremating) corpses.
J A Topf und Soehne, Erfurt. The company had an established reputation for building efficient crematoria and other furnaces that reached very high temperatures using low-grade coal.
According to the German Wikipedia, in November 1944 the SS began dismantling the crematoria in the hope of reassembling them in Mauthausen. Shortly before the arrival of the Soviet Army in Auschwitz (27 January 1945) the SS blew up the gas chambers and the remaining crematoria - and then fled.
Please see the link below, which should answer the question as far as Auschwitz is concerned. Most of the larger concentration camps, such as Buchenwald and Dachau, also had crematoria, but they were smaller.
The crematoria were made by J. A. Topf und Soehne (Erfurt). The firm had a reputation for manufacturing efficient crematoria that used low grade fue.