There have not been Jewish Priests since the destruction of the Second Temple.
since the destruction of their Temple Jews pray in the place of sacrifices
After the destruction of the Second Temple, the largest Jewish communities in Judea were in the Galilee. Prior to that, they weren't.
The Jerusalem Temple was destroyed in 70 AD by the Romans. Its destruction marked the end of Jewish control over Jerusalem and the scattering of the Jewish people. This event is significant in history as it led to the diaspora of the Jewish population and the shift of religious focus from temple worship to synagogue worship.
Some believe that the dark stripes on the tallit (prayer shawl) are in memorial of the destruction of the Holy Temple.
The destruction of the First Temple in Jerusalem led to the exile of the Jewish people, the loss of their religious center, and the beginning of a period of diaspora and dispersion. It also marked a significant turning point in Jewish history and identity.
Nebuchadnezzar was definitely not Jewish. He was a Babylonian king who was responsible for the destruction of the first Jewish Temple.
That destruction which Josephus wrote was in the year 70 by the Romans.
The Jewish sacrificial system started with the building of the Tabernacle. It ended twice, first with the destruction of the first Temple to resume after the second Temple was built, then again after the second Temple was destroyed. The Torah specifies that when there isn't a Temple standing, prayer replaces sacrifice.
A synagogue is the Jewish house of prayer, similar to a church in Christianity or a mosque in Islam. Jerusalem is the holy city in Israel where the Temple stood before its destruction by the Romans. A Synagogues are meant to face Jerusalem, to remind us of the Temple while we pray,
Well the temple for Christianity is mainly at church.
That was the Babylonian exile, which followed the destruction of the First Temple in Jerusalem in 586 BCE.