re: How did the Germans know who was Jewish?

They didn't just kill Jews. They didn't just kill certain members from certain groups. Sure they wanted to get all the Jews, but they weren't crying if they 'accidentally' rounded up some Pure Germans and killed them as well. When you're hell bent on maintaining power and getting rid of your enemies, there will be a few missteps and accidental deaths.

You gotta break a few eggs to make an omelet.