the religion of the Jews
Judaism's real name, in English, is "Judaism".
Judaism.
adjective for Judaism is Jewish
If you mean "Judaism", they are known as "Jews".
Clergy for Judaism are called rabbis.
the word Judaism comes from the name Judah
the term "stateless religion" is not a concept in Judaism.
Yes indeed. Judaism is the name of the Jewish religion ... probably the best name.
Sarah, wife of Abraham, was one of the Matriarchs of Judaism.
It does not mean anything specific. Reform Judaism is one branch of Liberal Judaism. So, ostensibly, non-Reform would mean any other branch of Liberal Judaism or it would refer to Orthodox Judaism. This is not a commonly-used term among Jews.
That is like asking "Hey, my grandfather's name is Smith. Does that mean he's Catholic?" Judaism is a religion, not a race.
A Rabbi.