Jesus did not rebuild the temple.
Cyrus the Great.
The return from exile predated Jesus by over five centuries.
After defeating Babylon, Cyrus the Great of Persia allowed the Jews (and other people) to return to their homeland in 538 BCE.
A book of the bible did not allow anything, people did. If the question intends to ask: "In what book of the Bible does it discuss the return of the Jews from exile and the rebuilding of the Temple in Jerusalem?" there are two answers. The Book of Ezra and the Book of Nehemiah discuss this.
There was no 'church' and Israel was in northern Palestine. Hebrews who had been deported to Babylon by the Babylonians were allowed to return to Jerusalem to attempt to reclaim ancestral lands, and on the side rebuilt the destroyed temple.
If you are referring to the Ancient Holy Temple in Jerusalem, only Jews were allowed in. If you are referring to modern-day synagogues, anyone can enter.
They returned to Nazareth after their visit to Jerusalem.
Jews have returned to Jerusalem. However, there is no Jewish group seriously considering rebuilding the Temple as this would require destroying the Dome of the Rock Shrine of the Muslims and probably start a massive war.
yes herod's temple is in Jerusalem
Your question is ambigious. Jesus said our body is His temple.
Jesus was found in the temple in Jerusalem, known as the Temple of Jerusalem or the Temple of Solomon.
King Solomon built the first Temple in 957 BCE with resources provided by his father King David. The second temple was allowed to be built by King Cyrus of Persia while the Jews were exiled in Babylon (536 BCE). Cyrus made a proclamation that the Temple in Jerusalem would be rebuilt, and the surviving Jews would return to rebuild it. This edict was supported by King Darius (522-486 BCE) who followed King Cyrus. This is described in the book of Ezra.