Here "him" refers to Jeremiah. It is not clear why Jeremiah is referring to himself by name here. You may translate using first person, as the UDB does. (See: [[rc://en/ta/man/jit/figs-123person]])
Zekekiah uses a question to rebuke Jeremiah. Alternate translation: "It is wrong for you to continue prophesying and saying" (See: [[rc://en/ta/man/jit/figs-rquestion]])
Yahweh speaks of the city as if it were a small object that one person could give to another. The word "hand" is a metonym for the power or control that the hand exercises. Alternate translation: "I am about to put this city under the control of the king of Babylon" or "I am about to allow the king of Babylon to do whatever he wants with this city" (See: [[rc://en/ta/man/jit/figs-metaphor]] and [[rc://en/ta/man/jit/figs-metonymy]])