Did Jesus adhere to the religion of the Old Testament? [1] Did he follow Judaism strictly? [2] Why would he need a story book about himself to preach from when he would be here in the flesh? [3] Supposedly he created a new religion but he never wrote a word about that religion. Would he author an update if he came today? [4] Did he or his father decide on which bible writings are canon? [5]
Briefly, and in order:
[1] Yes.
[2] No, since Judaism at Christ's time had morphed into something very different from the religion of the Old Testament. The same holds true today.
[3] The New Testament was compiled as a record of his ministry and teaching, and as a record of the ministry and teaching of the apostles, for the sake of Christians in the countless generations to come. He preached from the Old Testament because he epitomized servant leadership, part of which is leading by example. It's extremely important to God that Christians know and understand scripture (Luke 16:29), and have a scriptural basis for everything they believe about God and morality (Isaiah 8:20, 1 Thessalonians 5:21). Christians should reason with each other on the basis of scripture (2 Tim 3:16-17).
[4] Without getting deep into the relevant scriptures here, God can be regarded as a family of two beings, the Father and the Son, perfect and like-minded in all respects. No one has ever seen or heard the Father. The Son, who is also called the 'Word', Greek
logos (which can also be translated as "spokesman") is the one who emptied himself and came in the flesh as Jesus Christ. He indicates in John 14:28 that the Father is greater than himself, in authority over him, hence "Father" and "Son". He is also the one who dealt directly with Abraham, the Patriarchs, Moses, and the prophets throughout the Old Testament, and is called the LORD or the Eternal. 'God' in the Old Testament, depending on the word used in Hebrew, can refer either to the God Family (i.e. the Godhead) or to God the Son. The distinction typically isn't important since the Father and the Son work in perfect harmony; anything commanded or effected by the Latter can effectively be regarded as commanded/effected by Both.
Scripture is written by men, specially chosen by God, by inspiration of the Holy Spirit, which is God's outflowing spirit, power, and essence. Hence while the individual authors' personalities and writing styles are their own, the substance of scripture--everything important--is of God. Many scriptures make this plain, but 2 Tim 3:16-17 is again a good starting point. The bottom line being that God, including the Word who is Jesus Christ, can be regarded as the senior co-author of all scripture. The apostles (specifically James, John, and Peter) were also guided by God's Holy Spirit in selecting which writings were ultimately to become New Testament canon, to "bind up the testimony and seal the law" (Isaiah 8:16), and this much
is documented in scripture.
I understand your comment that "[Christ] never wrote a word about that religion" is basically asking: why did Christ, while in the flesh, not personally write the books of the New Testament, instead delegating to his apostles? One could equally well ask why He spoke via the prophets in the Old Testament. I personally know of no concise answer to this question, but I do know from scripture that it pleases God to involve us (the sons of man) in His work, in order to teach us, train us, give us real purpose, and instill within us His spirit of industriousness, creativity, and authorship. I can think of no better way to do this than to involve men directly in the revelation of His prophetic word.
With this as context, moving on to your question: "Would he author an update if he came today?"
If by "today" you mean "when he returns in his second coming", and by "author an update" you mean "add to mankind's revelations about God", the short answer is "I don't know.". The slightly longer answer is "He can do whatever He wants to, and I'm sure his decision will be the right one."
[5] I don't know how They sorted it out, or if They even
had to sort it out. One of a million things I'd like to know about God but isn't in the Bible, which means we presently don't need to know.