There is this biblical concept that you obviously haven't heard of called prophetic duality. Satan is the king of Babylon because he rules this world, which the Bible also prophetically refers to as Babylon since this present evil civilization originated from Babel.
That Ezekiel passage doesn't have to explicitly mention anything about Satan or a fallen angel because that history happens to be repeated in Rev. 12:7-9. Isolating Eze. 28 and Isa. 14 in an attempt to argue against biblical teaching only highlights your own ignorance of what is written in Isa. 28:9-10 about how biblical doctrines are like jigsaw puzzles and that a person has to get all the pieces and put them together to understand the whole picture.
You are completely wrong on the premise that Eze. 28:13-18 doesn't mention anything about Lucifer, Satan, or fallen angels for the following reasons:
1. Eze. 28:13 says this being was in Eden. It clearly isn't referring to the human ruler of Tyre. This is prophetic duality it work because this is where it transitions to giving the history of the being that truly ruled Tyre from behind the scenes.
2. The "king of Tyre" that was in Eden is the same serpent that tempted Adam and Eve.
3. The serpent that tempted Adam and Eve is identified in Rev. 12:9 as Satan.
4. Eze. 28:14-15 clearly says this same being was a cherub that was perfect until lawlessness was found in him, which clearly means this being was a fallen angel.
5. Eze. 28:16 says this being deceived other angels into helping him rebel against God. So now we see a fallen angel producing other fallen angels by deceiving them. This verse once again mentions a cherub that had turned rogue, so there is no doubt that the leading rebel was formerly an angel.
6. Rev. 12:4, 7-9 repeats the same exact history that is given in Eze. 28:13-18, only this time it actually identifies the main rebel by name.
The problem with your theology is that fails to understand the fact that at Eze. 28:17, the prophecy transitions back to prophesying against the human ruler of Tyre. As verses 13-18 clearly shows, this passage couldn't possibly have been referring to a human being because the history that is given in this passage took place long before Adam was ever created.