But notice, nobody is named "Satan" here. Also, why would Satan be the king of a city and not a global empire of evil?
Is the prince of Tyre different from the king of Tyre?
Ezekiel 37:24-25 KJV
And David my servant shall be king over them; and they all shall have one shepherd: they shall also walk in my judgments, and observe my statutes, and do them. [25] And they shall dwell in the land that I have given unto Jacob my servant, wherein your fathers have dwelt; and they shall dwell therein, even they, and their children, and their children's children for ever: and my servant David shall be their prince for ever.
Here David is both king and prince.
What about the Eden references?
Ezekiel 31:2-11 KJV
Son of man, speak unto Pharaoh king of Egypt, and to his multitude; Whom art thou like in thy greatness? [3] Behold, the Assyrian was a cedar in Lebanon with fair branches, and with a shadowing shroud, and of an high stature; and his top was among the thick boughs. [4] The waters made him great, the deep set him up on high with her rivers running round about his plants, and sent out her little rivers unto all the trees of the field. [5] Therefore his height was exalted above all the trees of the field, and his boughs were multiplied, and his branches became long because of the multitude of waters, when he shot forth. [6] All the fowls of heaven made their nests in his boughs, and under his branches did all the beasts of the field bring forth their young, and under his shadow dwelt all great nations. [7] Thus was he fair in his greatness, in the length of his branches: for his root was by great waters. [8] The cedars in the garden of God could not hide him: the fir trees were not like his boughs, and the chesnut trees were not like his branches; nor any tree in the garden of God was like unto him in his beauty. [9] I have made him fair by the multitude of his branches: so that all the trees of Eden, that were in the garden of God, envied him. [10] Therefore thus saith the Lord God ; Because thou hast lifted up thyself in height, and he hath shot up his top among the thick boughs, and his heart is lifted up in his height; [11] I have therefore delivered him into the hand of the mighty one of the heathen; he shall surely deal with him: I have driven him out for his wickedness.
Here the Assyrian ruler (and apparently the Pharaoh of Egypt as well) is a tree in Eden and the other trees envied him. Trees are symbolic of rulers and nations in God's Garden (since God planted the nations and establishes the rulers, the world is likened to God's Garden that He manages).