After about 150 posts, it looks like the OP still hasn't really been addressed. Briefly I'd like to do so, without giving specific references. SAM can follow up.
1. How many people died at the hands of the Nazis?
I'm not sure. The figure usually given for the Jewish persecution is about 6 million people. Then you need to add groups such as gypsies, homosexuals, disabled people and others. There are approximate figures available.
2. How was the religious identity of the victims determined?
Jews were originally required to register for identity cards under the Nazi regime. This led to all Jews being required to wear the star of David prominently on their clothing. People who tried to hide were often dobbed in by their neighbours in the xenophobic society.
3. What are the records used to study the holocaust?
Personal diaries. Official government records. Letters and other correspondence. The Nazis, in particular, were sticklers for record-keeping. Records were often kept in triplicate at different locations.
4. Who kept these records?
Individuals kept their own personal diaries and letters. Government offices kept government records. Military records were kept by the military.
5. How was the authenticity of the records determined?
By the same processes that are used to investigate the authenticity of all historical records. There is a large literature available on this topic. For example, if two or more independent records attest to the same event, chances are that the event occurred. That's just one example.
6. What is the evidence supporting the desire of Germans to eliminate the Jewish population?
Statements by Nazi leaders, including all of the people with the highest offices, such as Hitler, Himmler, Goering, etc. There are plenty of recordings and written records of speeches given by Nazis. Add to that innumerable letters, sets of written orders and administrative documents.
7. Where did the 6 million figure come from?
One very obvious way to make the estimate is simply to look at records of who lived where in 1933, say, and then look at the populations of the same places in 1945. The missing people must have either left or died or been killed. In short, 6 million people are difficult to hide.
8. Which records are available to the public?
Practically all of them, as far as I am aware.
9. What is the evidence of the methods used by the Nazis?
Personal diaries. Official government records. Letters and other correspondence. The Nazis, in particular, were sticklers for record-keeping. Records were often kept in triplicate at different locations. There was also a lot of physical evidence, such as the actual concentration camps and death camps liberated by allied forces at the end of the war.
10. What efforts were made to compensate other victims of the Nazis?
I don't know about that.