You answered your own question. It was the Babylonians.
The Babylonians.
Yes, Nebuchadnezzar destroyed Jerusalem and enslaved the Hebrews.
Cyrus, king of Persia, issued an edict inviting the Jews to return to their land from the Babylonian Captivity.
Jerusalem was destroyed for the first time in 586 BCE and again in 70 CE.
Yes. Modern Judaism, rabbinic Judaism, grew from the Judaism of the rabbis in the great academies of first millennium Babylon and Palestine (where the Talmud was written). These academies were founded by students of the Pharisees after Rome destroyed the Temple in Jerusalem, and with it the sacrificial cult of the Temple. The Temple, in turn, was rebuilt after the end of the Babylonian Captivity by Jews returning from Babylon. The Temple in Jerusalem was originally founded as a home for the sacrificial rituals described in the Torah, which was the Holy book of the Hebrews at the time they occupied Jerusalem. Note, of course, that this is the evolution of a religion. I strongly suspect that the Pharisees of 2000 years ago would be as surprised by modern Judaism (in any of its forms) as Paul the Apostle would be surprised by modern Christianity (in any of its forms).
Titus led the attack on Israel that eventually destroyed Jerusalem and caused the Jews to be sent into exile for 1,878 years.
Jerusalem
There were a number of different Ancient Israelite and Judean capital cities, such as Gibeah, Hebron, Jerusalem, Shiloh, Samaria, etc. Additionally, the Kingdom of Israel and the Kingdom of Judah were two separate countries which (naturally) each maintained a distinct capital.
Jerusalem
jerusalem
Most likely no. Daily prayer in Judaism wasn't instituted until after the ancient Temple was destroyed in Jerusalem, in the year 70.
In the Temple in Jerusalem.