"Judah" refers to the southern kingdom of Israel. "Jerusalem" was its most important city. The names of the places represent the people who live in them. Alternate translation: "those living in Judah and Jerusalem" or "the people of Judah and Jerusalem" (See: [[rc://en/ta/man/translate/figs-metonymy]])
This is an idiom and refers to the time when each king reigned. They reigned one after the other, not all at the same time. Alternate translation: "when Uzziah, Jotham, Ahaz and Hezekiah were kings of Judah" (See: [[rc://en/ta/man/translate/figs-idiom]])