Why does it specify the day and month? Above (1), it specified only the month!
Malbim citing Mahari: This is to teach that it was 59 days after they made the foundation for the Heichal on the 24th of the ninth month. He had prophesized then about the completion of Malchus Paras; which lasted 59 years. Our verse informs that there was an interruption of 59 days in between ? a day for each year.
What is the source for the names of the months?
Radak: We find them here and in Megilas Esther, but not in other Seforim of Tanach. Perhaps they are Arame'ic.
How did Devar Hashem come to him?
Radak: An angel came to him and spoke with him, and showed this vision to him, like it tells.
Why does it repeat the names of his father and grandfather? Verse 1 already taught them?
Malbim: Their merit caused him to have such elevated prophesies.
