son ... son’s son - (2Ch 36:20). Nebuchadnezzar had four successors - Evil-merodach, his son; Neriglissar, husband of Nebuchadnezzar’s daughter; his son, Labosodarchod; and Naboned (with whom his son, Belshazzar, was joint king), son of Evil-merodach. But Neriglissar and Labosodarchod were not in the direct male line; so that the prophecy held good to “his son and his son’s son,” and the intermediate two are omitted.
time of his land - that is, of its subjugation or its being “visited” in wrath (Jer 27:22; Jer 25:12; Jer 29:10; Jer 50:27; Dan 5:26).
serve themselves of him - make him their servant (Jer 25:14; Isa 13:22). So “his day” for the destined day of his calamity (Job 18:20).