King David has been given verfication. Solomon was purported to be his son.

[biblicalarchaeology.org]

It is perhaps best , not to regards the Bible, OT or NT as a written document anyway. It is most probable, that it is more of a document that was edited into existence. Like a scrap book where editors, also nameless, took bits from here and there and pasted them together. We know that that certainly happened in the case of the later, New Testament, in its later days, and also with the Koran, much though Islamic zealots may claim otherwise, so it is reasonable to think that that is also true of the OT.

No, I don't think so, just about every original copy and document produced at the same time, has been found researched and studied to within an inch of its life, over the last few centuries. And no one got anywhere, except to say, that we are less sure now than we were two centuries ago. Short of something really massive, like a whole bunch of much earlier dead sea scrolls turning up, which is unlikely, it is not going to happen.

And in any case you are dealing with an age before, copy rights, before medical records, and even before birth and death certificates, there simply was not the documentation made, back then about people lives, or referencing who wrote what. In part because, when all documents were hand made on expensive materials, then they were only used sparingly, and then the chances of them surviving and not even being recycled, are vanishingly remote.

PS. Even the mainstream churches, such as the Roman Catholic, and the Church of England, admit that Moses almost certainly did not write the books that go by his name, ( since they refer to events after his death, such as his funeral, bit of a give away.) And that the New Testament, was certainly not written by Mark, Luke , Math, John.