('scholar' is intellectually dishonest and doesn't actually care about facts, but I provide the answers for the benefit of honest readers.)
'scholar':
Why is it that scholars cannot resolve the 586 or 587 BCE controversy?
Fallacy of division, loaded language. The 'controversy' (a difference of one year based on ambiguity in the source materials available during the 19th century) exists because although modern scholarship favours 587 BCE (the correct year), some sources defer to the older (mostly religious) traditional dating without reviewing all the available information. No scholars independent of JWs support 607 BCE.
Why can scholars not precisely determine the beginning of the 70 years?
Religious scholars are divided on whether the number should be interpreted literally or figuratively (a fault of the ambiguity in the source materials). If interpreted literally, the period necessarily began in 609 BCE, 70 years before the definite end in 539 BCE. Babylon definitively removed the last vestige of Assyrian power in 609 BCE.
Why is it that scholars cannot agree as to an understanding of the 70 years
A combination of ambiguity in the source materials and fallacious (mostly religious) appeals to tradition.
How is it that nowhere in the Bible does it state that the 70 years was a period of Babylonish domination?
The question is predicated on a lie. Jeremiah 25:11-12 explicitly identifies the period has one of servitude to Babylon, as does Jeremiah 27:1-11 and 2 Chronicles 36:20.
Why do scholars ignore the clear testimony of Josephus' discussion of the 70 years?
This question is also predicated on a lie. Historians do not ignore Josephus (who wrote centuries after the events in question), but they balance his statements with contemporary Neo-Babylonian records, as well as other statements from Josephus himself:
- Against Apion, Book I: "These accounts agree with the true histories in our books; for in
them it is written that Nebuchadnezzar, in the eighteenth year of his reign,
laid our temple desolate, and so it lay in that state of obscurity for
fifty years; but that in the second year of the reign of Cyrus its foundations
were laid"
- Antiquities of the Jews, Book X: "Containing the interval of one hundred and eighty-two years and a half. From the captivity of the ten tribes to the first year of Cyrus."
Why do scholars ignore the missing 7 years of Neb's reign?
Red herring. There are no missing 7 years as the story in Daniel is not a historical account. However, even if it were historical, the total duration of Nebuchadnezzar's reign (inclusive any '7 years of madness') is the same in the JW chronology. JW chronology also does not specify any specific 7 year period. The Bible's references to Jehoiachin's release from prison in the first year of Evil-Merodach makes it impossible to add 7 years to the total length of Nebuchadnezzar's reign.
Why is it the case that no peer review of Furuli's analysis is published in academic journals?
Furuli did not submit his work for peer review. It is self-published. Where Furuli's views are mentioned by scholars, they are rejected.
Why is it the case that critics of Furuli's research do not use the same methodology that has produced conflicting results?
Furuli's claims about the lunar observations are demonstrably false. Honest assessment of the observations necessarily conflicts with Furuli's dishonest 'findings'.
How do scholars account for the Babylonian gap of 20 years between secular and Bible Chronology?
Scholars recognise that there is no "gap of 20 years". For the Neo-Babylonian period, 'Bible chronology' is consistent with secular history. It is only the fringe JW interpretation that is contradictory.