This chapter is pretty straight forward. It prophesied the fall of Babylon.
The falled of Babylon did not happen slowly, it happend on just one night, recorded by Daniel in Dan 5:30-31. Darius the Mede may be another name for Cyrus the King , or a co-regent or captain of the army of Cyrus.
v6: God gave the Jews into the hands of Babylonians, however the Babylonians did not show mercy to the Jews, so God is punishing Babylonians by raising the Persian kingdom.
v8: Babylon is portrayed as the queen of the kingdoms (v5, v7), she thought her power would continue forever (v7). This queen became a widow who lost all her children (v9) when Persians conquered them.
Babylonians are idol worshippers, they worshipped Bel and Nebo (v46:1). They also believed in sorceries, magic spells (v12), and stargazing (v13). Today we still have people who believe in Horoscopes. As Christians, we should not believers in Horoscopes, we should not look to the stars to predict future. Instead we look to the Creator of these stars and marvel at His creation! We should definitely stay away from Sorceries and witchcraft. I would not even want to watch and read Harry Porter. Do not let our children read and watch Harry Porter, because sorcerers are portrayed as good and heros in these books and movies.
As we read the fall of Babylon in OT, we should always think about the fall of Babylon in OT, prophesied in Revelation Ch. 18. John must know the OT very well, and he allured to Isaiah 47 when he wrote Rev 18. Rev 18:7 says [I sit as queen; I am not a widow, and I will never mourn]. Babylon is a symbol of the worldly kingdoms that capture the heart of Christians. These worldly kingdoms will be destroyed forever before the Millennium Kingdom.