I can give examples about why these assertions are not only unfounded but, as is typical to Islam, they are distorted. It is curious that they would even grant that the Bible can be examined and consequently is misinterpreted since in Islam they believe the Jews and Christians are liars and corrupters. Islam brings rigid fundamentalism in every facet of its tradition in distinct contradistinction to Christianity. The original Christians (the Church) never thought of the Bible as being literal or some sort of book that fell out of the sky (as do modern day protestants). By definition that is what it is in Islam, and why they are so simplistic all the while projecting so much of their own baggage that makes little or no sense.
Islam's obvious thievery and assimilation of Jewish and Christian ideas is extremely obvious to anyone who studies history and also has studied Islam. The concept of someone who is fully God and fully man makes no sense to them. This mystery of God is not supposed to be logical. Similarly, because there is not conflict between reason and God (reason just can't explain the boundless, obviously), it does not make us stumble. If you know physics, you know that light is a wave and a particle. It exhibits both properties, which has been a conundrum for as long as it was "understood". This makes NO logical sense. Yet it is the reality. I don't want to get tangential, but do want to help address your questions. Quickly, then I will respond more later:
The most cursory study in Judaism would recognize that "Ego eimi o wn" (I am what I am, or, I am the one that is) or just "I AM" in the Old King James Version is the tetragrammatron, YHWH, the name that should not be spoken.
The problem with Islam is that it tries to understand other things through itself. That prism is not useful, especially since it is unfair and biased, regardless of your opinion of it. One has to see what the Christians say, and if that makes sense, then accept it or reject it. For example, if Jesus Christ is truly human, AS A HUMAN he in fact does have limited knowledge. When he was learning to write, paint, work with wood, construct sandals, whatever, do you think he was a superman wiz kid from an early age? In his humanity he is just like us save for one thing ( he does not sin).
Many of the biblical accounts show his humanity for a reason, and they attack these. In Christianity, human beings cannot be saved unless Jesus Christ heals the relationship that they broke with the one true God (God the Father), a break which disrupted their communion with Him. Think of it: What is the point of Jesus coming if it is NOT to show his humanity (which is complete)? God could just snap his magic fingers, there would be no need for Him. But then why create beings in the first place? Islam can't answer any of these questions and really has no idea what God is doing, or has done, or will do.
A few random questions
How did Jesus see "Satan fall like lightning from Heaven" (Luke 10:18)?
Again cursory knowlege of the Jews, and why the leaders wanted to kill him: Who can forgive sins but God alone? Why would Jesus state this over and over again if he were not God. Both parties were very aware of it.
The reality is that they don't understand the persons of the Trinity. In life we have order (Father/Son) because that is the intrinsic nature of the divine as well as what we see in our created world. They try to always oppose them, which is not necessary.