BackseatDevil:
The "fall of Jerusalem" is technically around 586
The 19th year of Nebuchadnezzar, including his accession year, is quite definitely 587 BCE (unless you also shift the year for the beginning of his reign). This is confirmed by the non-accession reference to his 18th year for the same event. Definitely not 586 BCE.
Now, if you consider how long it took to get the Jews OUT of Jerusalem, you can imagine that it would take less time to get them back IN their dear city... but still take a couple of years, at least... past 537.
There is no reason to conclude that those who were first allowed to leave Babylon would take years to return to Jerusalem. Many Jews remained in Babylon, so it is neither necessary nor valid to try to determine how long it would take all of them to return. Those who left Babylon at the first opportunity after Cyrus' decree (which is misrepresented in the Bible as being specific to Jews) could be back in Jerusalem in as little as four months.
This is made apparent as they didn't start working on the foundation of the second temple until 520.
No. That claim isn't supported by either the Bible or Josephus (Against Apion, Book I and Antiquities of the Jews, Book XI). The foundations were laid in 537, then work was slowed by opposing forces, and then halted by Cambyses II ('Ahasuerus'), and building resumed in 520.
Also " 537 + 70 = 607" is going BACKWARD in time.
I think everyone with even a rudimentary understanding of the subject is aware of that basic fact. It's not clear why you think that's a problem. But if you prefer, it could be phrased as -607 + 70 = -537. In either case, the JW doctrine is still completely wrong.