Why is the Bible divided into Old Testament and New Testament?

It is important to take note that there are assumptions in some of these answers. I would make a few points to stimulate thinking on this question.

1. The division, with a page, of the Tanakh/Hebrew Scriptures (OT) and the New Testament (Greek Scriptures) were not made under the inspiration of God (just as the chapters and verses are not, and perhaps some titles).

2. Jesus spoke of the New Covenant but never "the old". The term "old testament" was used once and "first testament" twice in the epistles. They didn't refer to the scriptures, but the covenant. In fact, the NT uses the term scripture or scriptures 53 times--this was how the apostles named the scriptures. Peter referred to Paul's extant writings as scripture while referring to the Tanakh (Gen to Mal) as scripture--he made no distinction. (True, when Moses put the first writings in the ark, it was referred to as the ark of the covenant or the ark of the testimony, but this was only the 10 Commandments or the 10 Commandments and the Book of Exodus).

3. All the apostles and Jesus considered the "scriptures" to be the Law and the Prophets or Moses and the Prophets, etc. This has been abandoned--but it is the biblical way of referring to the scriptures--the actual name. The word Tanakh is the acronym of Torah, Nevi'im, Ketuvim: the Law, Prophets, Writings. This is the shorthand way to say it. This would be closest to the way Jesus would refer to the scriptures. (Along this line, speculation alert: he might call the NT in its entirety, the Gospel)

4. I couldn't disagree more strongly against this opinion/doctrine, but some/many hold that everything that occurred in the Gospels was old covenant and must be disregarded as our rule for living under the new. In this case, all the Gospels should come after Malachi and the separation should be with perhaps Acts.

5. The dividing page is entirely man-made in that no books were in existence in the first century; all scriptures were in rolls and they would be kept together without distinction. Many books would require more than one scroll. Obviously, since the writings of the NT did not come in the order of the Bible today, we don't know if they were combined in unexpected ways: perhaps a scroll with some letters of Paul and Peter and a Gospel. We just don't know. There were pocket gospels available in the second century.

6. Heresy entered the church early. Marcion, who hated YHVH (the demiurge) with a dark passion is credited with popularizing the term Old Testament because these scriptures were evil and the God in them was evil--distinct from the God of the NT. Early, the church became virulently anti-semitic (John was discriminated against, as is written in his epistle). The desire to put a division between non-messianic Jews and Gentile Christianity as it grew, was immense. Christian writers after the first and second century exude hatred toward the Jewish people. This lasted for millennia.

7. If time and covenant were to be the division standard: There were hundreds of years between Genesis and Exodus--we don't have a division there (400 between Malachi and John the Baptist). If distinct covenants were the standard, then we would have more divisions: especially the Abrahamic, Mosaic, Davidic.

8. Regarding the question: "Why are the books of the New Testament attributed to people who probably didn't write and likely couldn't read?" I don't understand if the question is sincere. Of course, the scriptures were written by people who could write. Writing was in existence before Moses. Moses could write. The Hebrew's/Israeli's culture was based on their religious beliefs--directed by a God who gave His word to His people in written form--the only systematic, historically accurate history written by a "religion". The emphasis on the entire people mastering the scriptures was immense: this includes reading the scriptures, the writing of which is an integrated discipline. Because some of the apostles were fishermen or carpenters, in no way implies illiteracy.

First, it's helpful to know the old-fashioned meaning of the English word, Testament. Throughout the centuries, a person with an estate (buildings, land, and/or possessions of some worth) would write out their "Last Will & Testament" which had to be witnessed and signed and dated by two people of sound mind, to testify that what the person had written was how he wished his goods to be divided up between various benefactors after his death, and that he was of sound mind when he wrote down his requirements. A person doing that was called 'the testator', had made a legal document that had to be carried out after his death. Nothing could be done until he had died, of course. That is a critically important point with regard to the Bible.

To begin with, there only were the manuscripts written in ancient Hebrew that pertained to the people of Israel, though the Gentile nations were written about a lot as well. That collection grew from the first writings (done by Moses, circa 1400 B.C. at the latest.) through various kings and prophets of Israel, the end of that growing collection being written by the prophet Malachi circa 433 B.C. The Jewish people who meticulously kept and copied those manuscripts did not call them "the Old Testament", but the collection was know as the Tanakh.

After Malachi, there was a gap of about 400 years before Jesus was born. After Jesus' death and resurrection, his followers finally understood the connection between the ancient Hebrew writings that foretold a Messiah, and Jesus being that one. His resurrection made everything clear. Some time after that, the apostles began to write the account of Jesus' life, death and resurrection (the gospel accounts), and there quickly followed a batch of other manuscripts (all in koine Greek) giving the story of the new Christian church and how it was to maintain the faith once delivered to them, plus containing prophecies for the future.

Once both sets of writings were put together (a necessity for Christians to understand just who their Christ was), the clear distinctions between the ancient times up to Malachi, and the new times from Christ's advent till near the end of the first century warranted classifying both sets of writings as we now have them - the Hebrew scriptures were called The Old Testament, and the Greek scriptures were called The New Testament. The date for that might have been after Marcion drew up his own truncated, anti-Jewish list of Christian Scripture (circa A.D. 201) for that was what prompted a final, settled canonical list of scripture.

Both sets (the Hebrew and the Greek manuscripts) were about God's legal requirements for his people, with God himself telling the Jewish people that he would make a new covenant (or, 'testament') which would include the Gentiles far more than ever the previous (old) covenant had done. The old was always stated by God to be that which would lead into the new. He had always made clear that no sinful human could ever keep the old law covenant, and breaking it would put those people under a curse. The Messiah came to redeem God's people from the curse of the Law by fulfilling it.

Once fulfilled, it had served its purpose, so Christ died, and that was when the terms of the new testament (covenant) started to take effect. Christ opened up an inheritance for Jews and Gentiles, through faith in his death. That is why the book of Hebrews says that "the law made nothing perfect, but the bringing in of a better hope did; by the which we draw nigh unto God... By so much was Jesus made a surety of a better testament" (Hebrews 7:19 & 22). This is where the necessity for Jesus' death and resurrection is spelled out for us:

"But now he hath obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which we established upon better promises. For if that first covenant had been faultless, then should no place have been sought for the second. For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah: Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord.

For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people: And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest.

For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more. In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away...

How much more shall the blood of Christ, who through the eternal Spirit offered himself without spot to God, purge your conscience from dead works to serve the living God? And for this cause he is the mediator of the new testament, that by means of death, for the redemption of the transgressors under the first testament, they which are called might receive the promise of eternal inheritance. For where a testament is, there must also of necessity be the death of the testator. For a testament is of force after men are dead: otherwise it is of no strength at all while the testator liveth. Whereupon neither the first testament was dedicated without blood.... and without the shedding of blood there is no remission." Hebrews 8:6 to 9:22 A.V. (bold emphasis mine.)

This answer your first six specific questions; I don't know the answer to the seventh.

1. The events, or historical division happened at the time of Christ's arrival. The New Testament books, of course, hadn't been written yet. The New Testament books were written after this event, and the canonization of Scripture happened later, by the fifth century A.D.
2. Because Christ is the fulfillment of the old Testament
3. Absolutely! The Old Testament dealt with the old covenant, which was the promise between God and His people based on obedience to Mosaic law. The New Testament is based on God's promise of eternal life, based not on man's ability to keep the law (we can't) but rather on the perfection of Christ and His substitutionary sacrifice. The division between the two marks two distinct covenants, the one replacing the other.
4. Sure, that's one way of looking at it. You might be interested in Why are the books of the Protestant Bible in the order that they are in? for a less simplistic view.
5. I'm sure that they are intentional. One is, after all, older than the other. (Implying that the other is the new one.)
6. Yes. Christ is the turning point. It is upon Him that all of Christianity is based.
7. (crickets chirping.) I can't answer that one. I'm not aware of any, but it's impossible to prove the non-existence of anything. But, remember that the Bible isn't one book, or even 2 - but rather 66 (or 73 if you're Catholic!). To not have a division is to misrepresent what these things are. It would be akin to going to a library and finding all the books shoved into one.