Whether or not John wrote anything is not relevant. I have no reason to doubt the story concerning him. I believe the Bible to be a faithful record (scholars desiring to cast doubt on it notwithstanding). You may ask what motive would scholars have for denying the divinity of Jesus Christ. The answer is in a mirror.
This is patently false. Scholars base their opinions and supposition on historical data. But the real problem is that no one can prove that anyone or thing is divine as that would mean it was of God. Since God cannot be proven, that means you cannot prove Jesus was divine. You can believe he was. But you cannot state this as fact.