These are good questions, and as you have discovered scholars are all over the map in their answers. Most people agree that the setting of the story is roughly in the Patriarchal era (2000-1800 B.C.?), which suggests that, like the stories of Genesis which Moses wrote down, even the earliest date of composition would have been a lengthy time after the events described. Indeed, some Jewish traditions identify Moses as the author, while others associate it with the Solomonic period. Still others place it later, for a variety of reasons. As Grant, alludes to, there are complex debates about the form of the Hebrew of Job, which is certainly hard, but those need not detain us here. If Job lived in the region of Paddan Aram, rather than in Israel, there may be dialectal differences that complicate such analyses.
Like Genesis, there may have been pre-existing oral or written records of some kind that were then utilized by the Biblical author. In the same way, the Chronicler utilized Samuel and Kings several centuries later to write his own history of Israel and Judah under the inspiration of God. So "late" need not be a pejorative term, if we understand it properly and not (as the critics so often imply) as meaning "fabricated" and "erroneous". "Early" or "late", it seems that the process of composition would have had to be broadly similar, since it seems unlikely to have been an eyewitness account.
As to the words of the debate in Job, and potential overlap with Psalms (or Proverbs), the topic of the Old Testament use of the Old Testament is a hot research topic right now. It is obviously more complex than the NT use of the OT, since the direction of borrowing cannot always be assumed or proved. And of course, not everyone agrees when borrowing has actually taken place. I haven't studied the specific arguments for Job. Do you have verse references? In the case of the Book of Job, there is also a wider discussion as to whether the book is a verbatim record of the conversation between Job and his friends - not least since the entire debate is conducted in poetry! Is it possible that the author has recorded the flow of the argument accurately under the Spirit's guidance but placed the ideas of the speakers in poetic form? In that case, I think the test would be that the participants on reading the book (in heaven!) would recognize the debate as a fair representation of their points.
I'm not sure we can resolve the issue of the date of composition completely, which likely means that we shouldn't worry too much about it. We may be confident that it is an accurate account of the events described, like the rest of the Scriptures, whenever it was first written down. I hope that helps.
PS Even if the Book of Job uses material from the psalms, that does not necessarily mean that it dates from after the collection of the psalms into the Biblical book, which occurred after the exile. Many of those individual psalms existed long before the book, including one written by Moses himself (Ps 90). So in the case of dating relative to (the Book of) Psalms everything is more complicated. We know that Job's story at least was known to Ezekiel (see Ezek. 14), but again that doesn't necessarily prove that it was in the form of the current book.
