interesting questions, concerning Islam, Judea-Christian being the same God. But is not so, as Muhammad created the Islam faith by reforming the Arab polytheism, and adopting one of the Arab gods, "Allah". Muhammad also adopted the polytheistic temple Kaaba to be a center of the faith.
Initially, pre-islamic Allah had 3 daughters, here is a link to one of them,
http://en.wikipedia.org/wiki/Al-%E2%80%98Uzz%C3%A1 . Then this was denied as false, and Islam requires the claim Allah begat no one, as Islam cannot tolerate Christ as a possibility of being begotten of God.
The time of Muhammad, Christianity was gaining ground, the Jews were dispersed in many Arab communities, and Zoroastrianism still had influence. The Arab polytheism, was loosing ground.
Muhammad and his follows claim that they are the same God, so as to make a "newer is better" claim. Most Christians and Jews who are educated do not accept this, as the Quran text is clearly the work of a lunatic, and the literary quality compared to the old and/or new testament is lacking. The history of the early fathers taught by Islam is frequently out of sequence. This is due to the Arabs limited understanding of Judaism as well Arab culture that did not have understanding or practice of placing history in chronological order.
Muhammad wanted to unite Jews and Christian under Islam, and gain their wealth. When Muhammad was unsuccessful, the first war, and violence between Jews and Muslim began.
http://en.wikipedia.org/wiki/Invasion_of_Banu_Qurayza. So this is where the war started between Islam and the Jews.
Zoroastrianism is truly interesting from a comparative aspect to Judaism and Christianity, and there is a better case that they share the same God, then Islam and the Judea-Christian faith. Zoroastrianism was an important part of Persia, which is now nearly defunct faith but still around in some parts of India. The Zoroastrians were persecuted or force to convert during Islam expansionism.