They were murdered because they were Jews. In your examples the men were murdered for being on the opposing side, and so a possible threat (unlike the women and children).
nope
In terms of technical, legal citizenship, that (presumably) became available to Jews in Germany upon their emancipation in 1871. This opportunity was revoked a mere 64 years later in 1935 with the introduction of the Nuremberg Laws. Citizenship in this sense is a modern invention.
What I meant above was citizenship in the sense of belonging to a particular group. A person could be a German in a legal or social sense, and I meant it in a social sense. The Jews were never seen as being "authentically" German. They were seen as a foreign people living on German land. This certainly contributed to the ease at which their legal status was stripped.
By the way, this attitude wasn't particular to Germany, but all over Europe, from Russia to France.
(Before anyone takes it seriously: this is a parody of how stupid the parent sounds.)