>>509493661 (OP)Historian here. I actually specialized in contemporary german history.
First, before anything, the holocaust was real. We have all sorts of evidence, from the actual camps being found by US and Soviet troops, to reports from the SS and Wehrmacht, to official telegrams between party officials to of course, the witnesses of both victims and criminals.
I have seen with my own eyes letters from Hitler and Ribbentrop, from 1938 discussing the plans to repress and discredit Jewish populations in recent annexed Austria.
The holocaust numbers are not exaggerated. What we have are Estimates from the low 2 million to the high 6 million. Those are Jews alone. We also gotta remember that other groups were targeted, specially Slavics, Poles, Roma and Homosexuals and those might bring the death toll to about 10 million.
Germany was not the only perpetrator. Italy, Hungary, Slovakia and other Axis countries took an active part in the holocaust. The Italians had their own camps, the Slovakians had their own death squad units
Due to the nature of this event, it's really hard to get a precise number. This was before the age of computers and information, a lot of people did not have papers, a lot of people lived "of the grid", a lot of papers vanished or got destroyed be it by the germans or by allied bombing/fighting.
The camps were not the only method of killing. The camps are responsible for about 50-60% of killings. A big chunk came from death squads that would decimate entire villages; the Wehrmacht would mark the villages and categorize the population and the SS would do the dirty job.
All over Europe, villages and towns would have 10 to 30 thousand people executed in mass graves in a single day.