Jewish Faith
The people who follow Judaism are Jews.
There's no such term as "chirstions" in Judaism.
the term "stateless religion" is not a concept in 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.
It depends on how strictly you define Orthodox Judaism. Orthodox Jews hold that their form of Judaism is the same form of Judaism practiced by the Biblical Patriarch Abraham. As a result, he is the Founder of Orthodox Judaism. However, Jews did not go around calling themselves "Orthodox" until Samson Raphael Hirsch coined the term in the 1800s as a response to the Liberal forms of Judaism (Reform and Historical-Conservative) that were contemporaneously developing.
Messiah.
Other than vaguely encouraging spirituality, mindfulness, and ethical behavior, there are really no similarities in either behavior, belief, or long term impact between Judaism on the one hand and the Vedic Religions (Hinduism, Buddhism, Jainism, etc.) on the other hand.
Back when Judaism was first Founded, all other religions were polytheistic. Judaism was monotheistic.
Among other differences, Judaism is monotheistic.
There is no such term in Judaism.
Monotheistic.
The term Judaism is the Jewish religion, it comes from the Hebrew word "Yehudah" or "Judah" and refers to those from province of Judea.