1. I have already explained why the term "begotten" does appear to be likely in the earliest texts, which are present, well at least in John 3:16. I have also explained that the Quran significantly misrepresents the Christian view of the incarnation, especially by what Christians mean when they say Jesus is the Son of God. Even then "only-born" is a better translation but most versions translate "one and only", because Jesus was conceived by the Holy Spirit, born of the virgin Mary.
Secondly, even if begotten is in the texts, Christians understand it to imply birth by woman but not necessarily conception of man.
2.
Mathematical and logical fallacy. Firstly what you are saying is like in induction when you have to prove for all n values. How I see your argument "If n=1 is true and n=2 is true then n=anything must be true."
It is like you trying to compare it to an analogy and failing. The Quran affirms that God can see without eyes, hear with ears, speak without a tongue; Christians agree, and also say that God can have a son without a wife; it is not that ridiculous. Your comparison to mathematical induction; is ridiculous, because I haven't assigned cases, or numerical values.
(Which you said was because people misunderstood what it meant...
People in the 16th century, we now have even more copies, of the New Testament. The same applies for 1 John 5:7, we have enough historical data, to piece together with a great deal of certainty what the original texts were. In fact, we can piece together the entire NT except something like 3 sentences of such, just from quotations in other preserved writings from the early church.
But the reason I can make that inference, is because it we say that God doesn't require what is NORMALLY EXPECTED for that to be the case, for the case of sight, hearing and speaking; why would God having a Son be any different??
But wouldn't God, if it was truly about his nature make it clear and concise so that there's no room for misinterpretation since it's such a vital topic of faith and can either lead to eternal damnation or eternal salvation?
That, if it wasn't for Christ, would make a strong case for atheism. Since if we take the Gospel seriously (and true), then we end up with the conclusion, that Jesus is indeed God, meaning that God has made his nature and character clear. Secondly, God has also made his nature very clear in creation; his divine power as well. Which brings me to this...
The only room for misinterpretation comes when you take a text/revelation that was revealed only to one person, as in every religion, except Christianity (see later down) that comes at least 600 years after the events occurred, comes and then says that the texts which are closer/closest in some cases to the events are corrupted and hence has to redefine or reinterpret what is fairly clear and make it vague:
e.g. "[Jesus said] All things have been committed to me by my Father. No one knows the Son except the Father, and no one knows the Father except the Son and those to whom the Son chooses to reveal him"
A. God created by the Word.
B. Jesus in the Quran, is called the Word of God.
C. Is the Word, therefore creator or creation?
4. The Bible wasn't collated until the 3rd century. The texts that make it up, already existed and were widely accepted and in circulation.
Also if we go by your claims by Jesus(pbuh) you have to verify every single thing he said and did?
No, I think it would be sufficient all I have to do is show that Jesus died and rose again. BECAUSE if that was not true, then he would be either a lunatic or liar.
This would show TWO things, one that the Quran does not give us the right view of Jesus (which is doesn't anyway, considering that statement A below is unanimously agreed by all historical scholars, with the exception of Muslims).
And that is enough to verify large amounts of the rest of what he said. The first is already verified in history as fact, and the second follows on logically, if you consider the accounts. The argument is very simple:
A. Jesus had to be dead & buried (in a tomb) - fact, historically verified, and medically consistent.
B. The tomb had to be empty - usually disputed, but there is evidence for that.
C. Jesus appeared to many people - also disputed, and there is evidence also for this, the earliest texts on the resurrection affirm the appearances to many, including Peter, the 12 and 500 individual people.
If I look up the arabic im 99%
These translations are done by Muslims or Muslim scholars. I have good reason to trust that the text, is very correct.
But if the Quran is from God then it would be more accurate than an inspiration.
Again the inspiration = from God. So don't know where the basis for your claim. Besides the Quran/Muslims, say that previous revelation FROM God was corrupted; so either its a circular argument, or has no basis for arguing the Quran's superiority.