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The Jewish temple in Jerusalem.
Jerusalem was the only place in the world that had a Jewish Temple at that time.
Your question is ambigious. Jesus said our body is His temple.
The empire that took destroyed the First Jewish Temple in Jerusalem (and defeated the Southern Kingdom of Judah) was Babylonia in 586 BCE. The empire that destroyed the Second Jewish Temple in Jerusalem in 70 CE, after defeating the Jewish Zealots was the Roman Empire.
The Kohenim (priests), however, they weren't leaders of the Jewish people, they were in charge of the Temple.
Chanukah (Hanukkah)
The First Temple was located on the Temple Mount in Jerusalem, the same location as the Second Temple.
Nowhere that I know of.
The Israelite/Hebrew/Jewish Temple in Jerusalem was destroyed by the Romans in 70 CE. It stood on the place called the Temple Mount / Har HaBayit, of which the Kotel ("Western Wall", "Wailing Wall") is the only surviving component. So there is presently nothing in the 'temple of Jerusalem', as there has been no temple of Jerusalem for over 1900 years.
For observant Jews there could only be one Temple: the Temple in Jerusalem. As a Jewish priest, Zechariah must have served in this Temple.
Jews worship at synagogues.
The Temple of God in Jerusalem, Israel, is located on the Temple Mount in the Old City. It is a significant religious site for both Jewish and Muslim communities.