Jamieson, Fausset and Brown on Jeremiah 29:3

3. Zedekiah ... sent unto Babylon--In Jr 51:59, Zedekiah himself goes to Babylon; here he sends ambassadors. Whatever was the object of the embassy, it shows that Zedekiah only reigned at the pleasure of the king of Babylon, who might have restored Jeconiah, had he pleased. Hence, Zedekiah permitted Jeremiah's letter to be sent, not only as being led by Hananiah's death to attach greater credit to the prophet's words, but also as the letter accorded with his own wish that the Jews should remain in Chaldea till Jeconiah's death.

Hilkiah--the high priest who found the book of the law in the house of the Lord, and showed it to "Shaphan" the scribe (the same Shaphan probably as here), who showed it to King Josiah (2Ki 22:8, &c.). The sons of Hilkiah and Shaphan inherited from their fathers some respect for sacred things. So in Jr 36:25, "Gemariah" interceded with King Jehoiakim that the prophet's roll should not be burned.