The word "I" and the phrase "the king" refer to the same person. The king is reminding the people who hear this letter that he is the author of this letter.
# to inquire concerning Judah and Jerusalem according to God's law
What they were to inquire about can be stated more clearly. Alternate translation: "to investigate the situation in Judah and Jerusalem, in order to learn whether or not they are obeying God's law" (See: [[rc://en/ta/man/jit/figs-explicit]])