I haven't yet found anything in the Scriptures about his personal family, but he had been transferred to Babylon about ten years before the actual destruction of the Temple.

God used to speak to the prophets by means of dreams and visions, as it written in Numbers 12:6. "If there be a prophet among you, I the Lord will make Myself known to him in a vision, and will speak to him in a dream.

Ezekiel's message was to the Jews in exile in Babylon, whom he would serve as a consolation and preservation of the people as a people in preparation for the end of the exile and return to the Land of Israel. (Ezek. 37:12)

Ezekiel was sent in advance to Babylon to serve as a channel of communication with Jeremiah in the Land of Israel to keep the hopes up of the People of Israel. So, they, Ezekiel in Babylon and Jeremiah in Israel would coalesce in a kind of partnership to not only prophecise agains the destruction of Temple but also to keep the people together for their return at the end of the 70 years of exile.

Most the people, as usual, did not receive his message too happily as an evidence that only a very small remnant returned to Israel at the end of the exile.

Ezekiel does speak about the Messiah, although not an individual Messiah, but the collective Messiah in the People of Israel, especially as he mentioned the metaphorical resurrection from the graves of the nation and return to the Land of Israel.