As to your question, Thyll: Islamic belief, clearly states:
(Translated from the Qur'an to English, Might sound a little diff. then biblical English, I believe)
In the name of Allah, the Beneficent, the Merciful.
112:1 Say: He, Allah, is One.
112:2 Allah is He on Whom all depend.
112:3 He begets not, nor is He begotten;
112:4 And none is like Him.a
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A very early part of the Qur'an, stating that nobody is/ever will be/ and more importantly does not need to be the son of God.
All "Prophets" in Islam are what they are said to be, and that is merely a "Prophet". (As, of course, Jesus can be revered to as God instead of a prophet to Christians, No?)
For your second question:
The birth of Jesus (you could say) divided Judaism itself depending on different beliefs. According to historians there were many people that believed Jesus was A) Prophet but confused, B) Prophet but not the son of God C) Fail Jew D) The Birth of Christianity -- Because of the differences, this was one of the reasons Islam was allowed to spread.
The Differences between Islam and Judaism are that
1) The History of the Torah is the same, but to Muslims it was, according to our prophet, messed up. As in what was taught was the word of Allah (Which wasn't Islam at that time, of course) -- but was changed to the Judaism of Jesus's time (IE: The sins and rabbis and whatnot, also)
2) The exclusiveness for the Jews, just like Christianity, was deleted -- So anyone could become a Muslim
3) The Holy Land = Holy, You don't have to live there at the end of the world
4) Kosher Food basically turns into No eating Pork/Drinking Blood/Drinking Alcoholic beverages/Cannibalism
[Being breif here, these laws didn't really just turn into other things, Lol]
5) Islam has its own rules, new language, etc. Very tolerant, more rights for Women just like Christianity -- Though in the poor world of Islam and the culture women have a bit of a lower status in regard to the west nowadays.
6) No Sons of God (I think the Torah talks about some prophet, named with an E in English being one)
7) Jews predict a Prophet, Jesus comes, Jesus predicts end of the world etc. -- Muhammad comes (At least, to the Muslims).
The Jews didn't accept Jesus, who was a Jew, and they certainly did not accept Muhammad, who was an Arab. To some people's belief the thought was that the Jews kept sinning, etc, so due to the marriage of Abrahams sons leading off to two semitic ethnicities of arabs and jews, the other son's ancestors basically ended up as a Prophet in Muslim tradition
8) Finally, there is a tolerance for "People of the book"/ People that follow any book delivered by God, and to Muslims, that would be Christians and Jews along with all those that branch from it and keep the same entity.
Also, these Judaism and Islam have both kept their idealistic belief of Monotheism whole to the entire world, while religions like Hinduism and Christianity cannot to the entire extent. (Tbh, With no offense, I've asked countless people to explain me the Trinity -- And I get countless different answers and sometimes not an answer at all but some turkish proverb)
Hope that helps.
Its hard to lay out all the differences, after all, I'm just forum posting here but I think I got most of it.