What is "Yolech Hashem oscha ve'es Malk'cha ... " referring to?
Rashi (in Melachim 2, 22:13): It is referring to Yoshiya ha'Melech, who was destined to go into Galus. 1
Ramban #1 (on Pasuk 42): It is referring to the exile of King Agripas to Rome 2 during the period of the second Beis-Hamikdash, which resulted in the Galus a short time later.
Ramban #2 (on Pasuk 42): It refers to the Chashmona'i king Aristobulus, who was exiled in chains to Rome. 3
Although in the end, it was his son Tzidkiyahu and his grandson Yechonyah, who went into Galus and not he ? See Pasuk 20 there.
Ramban: However, he returned to Eretz Yisrael together with an emissary of the Emperor of Rome, and proceeded to capture large swaths of land in Yehudah, at which point Pasuk 48 "Va'avadta es Oyvecha ... " materialized. Refer also to 28:49:3:1.
Seforno (14): This was during a civil war between two Chashmona'i kings (the brothers Hyrkanus and Aristobulus), when the latter was exiled to Rome at the hand of Pompei.
Why does the Torah add the words "Malk'cha asher Takim alecha"?
Ramban (Vayikra 26:16): The Torah writes this in connection with King Aggripas, 1 who was inellegible to rule (because he was a descendant of slaves), and whom the people nevertheless crowned as king. 2
What does the Torah mean when it writes "Va'avadta Sham elohim Acherim ... "?
Rashi (in Pasuk 64) and Targum Yonasan: It means that they will have to pay taxes to the priests of Avodah Zarah.
Targum Onkelos: It means that they will have to serve people who worship wood and stones.