How did they justify killing millions of people? Didn't anyone feel that something is wrong?
I'll let one of our resident Nazi Germany experts cover the justification bit, but will address your third question myself:
It's important to understand that not all Germans supported the Nazi Regime for a wide variety of reasons - some were organised groups of nobility, businesspeople and intellectuals (Kreisau Kreis and Solf-Kreis being the notable examples) ideologically opposed to the Nazi regime; some were military officers (most of the people behind the July 20 plot and the Oster Conspiracy) who disagreed with Hitler's military actions and strategies, and some were just people opposed to the concept of Holocaust - Oskar Schindler might be a name that rings a bell for most, but there were plenty of other notable Germans - Armin Wegner, Gustav Schröder, Wilhelm Hosenfeld, Karl Plagge and possibly hundreds and thousands of ordinary Germans who helped protect the Jews from persecution.
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