Short answers, pulled from the story.
The word Jew derives from the Hebrew name Judah, the fourth son of Jacob. Originally, the term referred specifically to the inhabitants of the Kingdom of Judah, distinguishing them from the Samaritans and gentiles, but by the late sixth century BCE, it had evolved to encompass followers of Judaism and citizens of Judea regardless of their specific tribal lineage.
The Babylonian exile ended in 538 BCE when the Persian King Cyrus the Great allowed the Jews to return. The Second Temple was constructed between 521 and 516 BCE under the leadership of Zerubbabel and Joshua the Priest.
The destruction of the Second Temple by the Roman general Titus in 70 CE stripped the Jewish population of political autonomy and shifted the center of Jewish life from the Temple to the synagogue and the study of the Torah. The province of Judaea was renamed Syria Palaestina, and the Great Revolt resulted in the death of hundreds of thousands of Jews, with some estimates suggesting the death toll amounted to about 600,000 Jews.
On the 14th of May 1948, upon the termination of the mandate, David Ben-Gurion declared the creation of the State of Israel. This declaration occurred immediately after neighboring Arab states invaded and were resisted by the newly formed Israel Defense Forces.
Hebrew was revived as a spoken language by Eliezer ben Yehuda, who arrived in Palestine in 1881. The language had not been used as a mother tongue since Tannaic times and was designated as the State language of Israel.