Here "mouth" represents speaking. Alternate translation: "Yahweh did what Jeremiah prophesied that Yahweh would do" (See: [[rc://en/ta/man/jit/figs-metonymy]])
This is the name of God that he revealed to his people in the Old Testament. See the translationWord page about Yahweh concerning how to translate this.
Here Cyrus is represented by his spirit. This speaks of Yahweh causing Cyrus to want to act as if he "stirred" his spirit. Alternate translation: "Yahweh ... made Cyrus want to act" (See: [[rc://en/ta/man/jit/figs-synecdoche]] and [[rc://en/ta/man/jit/figs-metaphor]])
The voice is a metonym for the message the voice speaks, and the kingdom is a metonym for the people whom a king rules. Alternate translation: "Cyrus sent a message to everyone over whom he ruled" (See: [[rc://en/ta/man/jit/figs-metonymy]])
This can be translated in active form. It might be best to translate so the reader understands that other people might have helped Cyrus get the message to the people over whom he ruled. Alternate translation: "what Cyrus wrote and what his messengers read so people could hear them" (See: [[rc://en/ta/man/jit/figs-activepassive]] and [[rc://en/ta/man/jit/figs-explicit]])