If Daniel was one of the Prophets, I do not understand why he is not counted among the Prophets.
Why is his book among the Ketuvim and not Neviim?
See this lecture by Rabbi Dr. Leiman.
The standard answer, that of Rambam, is that the exact level of Daniel's visions were always "Divine inspiration", but never quite over the threshold of "prophecy", though he must have been pretty close to the line. (The Malbim says, for instance, that Ezekiel only made it over that threshold occasionally.) Don't ask me exactly what the "threshold" is.
The alternative, suggested by Don Isaac Abarbanel, is that the books of "prophets" were those who were given prophecy to convey to the people at that moment, for some purpose. Daniel was an "armchair prophet" (to quote Leiman); while he had visions, he was never ordered to convey them. So he may have been a "seer", but not a "speaker."
The difference concerns what was originally intended to be written, versus what was originally intended to be announced orally to the people.
In the Moreh Nevuchim, Rambam explains the different levels of prophecy.
The second degree [of prophecy] is this : A person feels as if something came upon him, and as if he had received a new power that encourages him to speak. He treats of science, or composes hymns, exhorts his fellow-men, discusses political and theological problems; all this he does while awake, and in the full possession of his senses. Such a person is said to speak by the holy spirit. David composed the Psalms, and Solomon the Book of Proverbs, Ecclesiastes, and the Song of Solomon by this spirit; also Daniel, job, Chronicles, and the rest of the Hagiographa were written in this holy spirit; therefore they are called ketubim (Writings, or Written), i.e., written by men inspired by the holy spirit. Our Sages mention this expressly concerning the Book of Esther. In reference to such holy spirit, David says:" The spirit of the Lord spoke in me, and his word is on my tongue" (2 Sam. xxiii. 2): i.e., the spirit of the Lord caused him to utter these words...
This is different from the type of prophecy that the Neviim had - in a dreams or visions.
And different yet from the highest level, which only Moshe Rabenu achieved - to have a clear prophecy without the intermediary of a vision (mouth to mouth).
An academic answer would be that the division of the Tanakh into Torah, Neviim, and Ketuvim has to do with when the text was canonized. The Torah's text became stable around the time of Ezra, the Neviim around the time of transition from the Persian Empire to the Greek Empire, and the Ketuvim only after the destruction of Bayit Sheni.
This does not address the issue of 'dating' the material; the consensus of biblical scholars is that Daniel was composed at some point in the early Hasmonean era.