Did Manasseh son of Hezekiah kill Zacharia?

No. According to tradition, Menashe (Manasseh) killed Isaiah (Talmud, Yevamot 49b). Zachariah, son of Yehoyadah, was killed by an earlier king named Yoash (2 Chronicles ch.24). Not to be confused with the more well-known Zachariah, who lived at the beginning of the Second Temple and authored his own prophetic book.