According to Judaism, a Jew's nature as a Jew is part of his make-up and does not "wax and wane" with his belief. The nature of being part of the Jewish Nation - Jewish Identity, is not contingent on faith. (To a religious Jew, the question is as absurd as asking "How can an Italian who does not have faith in Catholicism resume his Italian-ness?") It is for this reason that Judaism does not recognize de-conversion or apostasy.
If a Jewish person who has been atheist or the adherent of a different faith wishes to rediscover their Judaism, there are numerous organizations that can assist with that and are sponsored by the different Jewish movements.
An Apostate Jew
A Jew that converts to another religion.
Somebody who isn't Jewish is a "goy" in Yiddish.
A Jew is someone born to a Jewish mother or who has converted to Judaism; Jewish tradition does not recognize "half Jewish" or "partly Jewish" as a status. You either are or you are not. A Jew who abandons Judaism and adopts another religion is an apostate. It is important to understand, though, that to be Jewish is to be accepted as a Jew by the Jewish community. It is not just between you and God. So, conversion to Judaism involves coming learning enough to come before a rabbinical court and be accepted as a Jew. There are also ritual requirements such as circumcision and dunking in a mikvah. For an apostate to return to Judaism, mere private renunciation of the other religion is not enough, it is also necessary to patch up differences with the Jewish community.
An apostate.
I suppose you call them either a Jew or a Muslim since Judaism and Islam are separate religions and you cannot be both. There is also no specific term for a Jew who converted to Islam or a Muslim who converted to Judaism in either religion. (Apostate is general term for abandoning your faith.)
Judaism creates Jewish identity. It means that each Jew has his/her people, has the Torah, has a 3,000-year heritage, outlook, beliefs etc.
A Jew is a person who is part of the culture or community that is based upon Judaism and whose origins can be traced back through the ancient Hebrew of Israel to Abraham.
What is this question all about?
Timothy was of mixed heritage; his mother was a Jewish believer, while his father was a Greek. This background placed him in a unique position within the early Christian community. Although he had Jewish roots through his mother, he was not considered a Jew in the traditional sense due to his father's Greek identity and the fact that he was not circumcised, which was a key marker of Jewish identity.
In Jewish law, a person is considered to be a Jew if his mother was Jewish. Whether or not an individual Jew observes the laws and traditions of Judaism is a matter for his own conscience, and doesn't affect his legal identity under the law.
No, Jew is the noun, Jewish is the adjective.