Haggai was a prophet who along with Zechariah encouraged the returned Jewish exiles to rebuild the temple in Jerusalem after the Babylonian exile 2500 years ago. Based on verse 2:3 in the book of Haggai, he may have directly witnessed the destruction of Solomon's temple.
Haggai was a prophet in the Bible, not much is known about his occupation outside of his prophetic ministry.
Haggai
The Book of Haggai is written by the biblical prophet Haggai. He was tasked with encouraging the Jewish people to rebuild the Temple in Jerusalem after their return from exile in Babylon.
Because the prophet Haggai told them, in the name of God, to do so.
Haggai was known as one of the minor prophets and served as such during the reign of Darius. Most of the prophecies of Haggai are concerned mainly with rebuilding the temples after the Babylonian Captivity.
Some say the object of the Book of Haggai seems to be to immortalise Haggai by giving him credit for commencement of the Temple, suggesting that the book was written much later when there were no longer any witnesses to refute the claim. On that view, Haggai could not have been the real author. We simply do not know.
Jeremiah
No, Haggai was a man. He was a prophet in the Hebrew Bible who lived during the time of the Babylonian exile and encouraged the people to rebuild the temple in Jerusalem.
Haggai is a prophet in the Old Testament who is known for encouraging the Jews to rebuild the Second Temple in Jerusalem.
Zechariah was a contemporary of Haggai, Ezra, and Nehemiah. They were all involved in the restoration of the temple and the rebuilding of Jerusalem after the Babylonian exile.
Daniel was alive at the time; and probably also Haggai, Zechariah and Malachi.
The prophet who coincided with Ezra and Nehemiah is Malachi. He is considered the last prophet in the Old Testament and his prophecies are believed to have occurred during the same time period as Ezra and Nehemiah's activities in restoring Jerusalem.