You are absolutely right that the Muslim claim that the Bible is corrupt is not supported by the evidence. We all know that the originals were copied, and that we do not have the originals, but the nearly 6000 copies of the Greek manuscripts we have gives us a huge trove of evidence which allows us to reproduce a nearly perfect Greek manuscript. They want to say that the Bible is corrupt so that they can claim that the accounts of the crucifixion of Jesus are not accurate, but any possible account of slight copying errors certainly does not bring into doubt the crucifixion of Jesus!
About your new question, the evidence for the gospel of John being inspired is exactly equal to the evidence for the inspiration of the synoptic gospels. We know from church history, specifically from the letters of the very early church fathers, that the gospel of John was considered inspired and canonical from the end of the first century onward. Besides, the internal evidence for inspiration is pretty much a slam dunk. The book of John is inspired by God. That is for sure. What is the logic of saying that, because it was written ten or twenty years after the synoptics, it is not inspired? What about the Hadith, which was written one hundred or more years after the Qur’an. Does that mean it is not inspired?
But, as you know, some Muslims, desperate for any possible way to discredit the claims of deity of the Bible, want to create doubt, by claiming that Jesus did not claim to be God in Matthew, Mark and Luke. Now, it is true, that in these three gospels, which record more of Jesus public speeches, as opposed to John, who reports more of Jesus’ private speeches, do not have nearly as many clear statements about the deity of Jesus, but they still have Jesus claiming to be God. In Matthew 1:23, Jesus is God-with-us. Also, in Matthew 3:17, God tells the people, “This is my Son, whom I love.” Again, even a demon recognizes Jesus as Son of God in Matthew 8:29. Jesus has not publicly proclaimed this yet, at least not in Matthew, but it has been declared, nevertheless. By Matthew 14:33, the apostles are nearly getting it. When Jesus calms the storm they worship him, calling him Son of God. For a faithful Jew, only God can be worshiped, yet Jesus does not refuse this worship. Finally, in Matthew 16:16, Peter gets it. “You are the Messiah, the Son of the living God.” Even the centurion at the cross got it, declaring Jesus to be the Son of God (Matthew 27:54). There is further indirect evidence that Jesus is God in Matthew. For example in Matthew 9:2-8, Jesus declares a man’s sins forgiven. Witnesses accused him of blasphemy because, as all Jews knew, only God could forgive sins. Again, even with plenty of opportunity, Jesus did not correct their error because they were not making an error. In Matthew 28:18-20 Jesus makes perhaps the most clear claim to deity in Matthew. He tells his disciples that he has all authority in heaven and on earth, as well as telling them to baptize in the names of the Father, Son and Holy Spirit–equating the three equally as God.
These examples are from Matthew alone. Similar cases can be made from Mark and Luke. Jesus did not openly say “I Am God” in the synoptic gospels, but he might as well have as far as we are concerned, as it is quite clear what is going on. The fact that the synoptics record mostly public preaching and John records mostly private or smaller group preaching, combined with John’s different purpose in writing his gospel explains why John has more clear statements by Jesus of his deity. Jesus was careful what he declared publicly in his preaching because he was well aware of exactly where and when he would be killed.