Judaism is a religion. 

Jews are of that religious group but some believe and some don't. 

Jewish women can marry non-Jews but then as at as I know their kids can't Jews. 

Why not not use a search engine to find more details?

Jews are a subgroup of the Semite race which encompass Arabs, Berbers, Persians and Turks among other smaller groups, the Semites native land is the Middle East and Northern Africa.

Judaism is the religion of over 80% Jews, the rest being Muslims or Christians. It is Judaism that forbids its followers from marrying outsiders, not being ethnically Jewish.

Is Chinese a religion? Can a Chinese man marry a foreign woman?

Seriously, Judaism is auto-transferred matrilineally. A Jewish woman has Jewish children with no further requirement. A Jewish man must actively teach his half-Jewish children the Jewish faith, and get them formally accepted. Otherwise thay aren't Jews. For this reason, Jewish women are protected, to avoid too many faithless Jews in the next generation. I'm not a Jew, but this is what I recall my friend telling me. His dad was Jewish, he wasn't a practicing Jew himself, so he's half-Jewish yet not considered Jewish.

Jew know what I think?  I'm still wondering how they got all those animals on the boat.  Noah was one crafty hombre!

https://en.wikipedia.org/wiki/Jews#Who_is_a_Jew.3F

Who is a Jew?Main articles: Who is a Jew? and Jewish identity

Judaism shares some of the characteristics of a nation, an ethnicity,[15] a religion, and a culture, making the definition of who is a Jew vary slightly depending on whether a religious or national approach to identity is used.[91][92] Generally, in modern secular usage Jews include three groups: people who were born to a Jewish family regardless of whether or not they follow the religion, those who have some Jewish ancestral background or lineage (sometimes including those who do not have strictly matrilineal descent), and people without any Jewish ancestral background or lineage who have formally converted to Judaism and therefore are followers of the religion.[93]

Historical definitions of Jewish identity have traditionally been based on halakhic definitions of matrilineal descent, and halakhic conversions. Historical definitions of who is a Jew date back to the codification of the Oral Torah into the Babylonian Talmud, around 200 CE. Interpretations of sections of the Tanakh, such as Deuteronomy 7:1–5, by Jewish sages, are used as a warning against intermarriage between Jews and Canaanites because "[the non-Jewish husband] will cause your child to turn away from Me and they will worship the gods (i.e., idols) of others." Leviticus 24:10 says that the son in a marriage between a Hebrew woman and an Egyptian man is "of the community of Israel." This is complemented by Ezra 10:2–3, where Israelites returning from Babylon vow to put aside their gentile wives and their children.[94][95] Since the anti-religious Haskalah movement of the late 18th and 19th centuries, halakhic interpretations of Jewish identity have been challenged.[96]

According to historian Shaye J. D. Cohen, the status of the offspring of mixed marriages was determined patrilineally in the Bible. He brings two likely explanations for the change in Mishnaic times: first, the Mishnah may have been applying the same logic to mixed marriages as it had applied to other mixtures (Kil'ayim). Thus, a mixed marriage is forbidden as is the union of a horse and a donkey, and in both unions the offspring are judged matrilineally.[97] Second, the Tannaim may have been influenced by Roman law, which dictated that when a parent could not contract a legal marriage, offspring would follow the mother.[97]

Jewing people over is definitely a religion in this country. That's all I can say...