The very question points to the need for suspended belief in fantasy/sci-fi. You're asking a logical question that can't really be satisfactorily answered because the answer itself is nonsense even within the rules established by the author.
Sauron was a Maia, an angelic being that is lesser in stature and power than a Vala, but still of infinitely greater power than any being of flesh and blood, whether man or elf or dwarf. Consequently, that a man or an elf, or a whole host of these, could overcome or vanquish a Maia is, at its foundation, a ludicrous idea. It would be like asking how an army of men could kill a single angel. An angel or a Maia (whatever you want to call it) is, for all intents and purposes, the equivalent of God Himself when it comes to the idea of a flesh-and-blood being fighting it.
So the idea of Sauron needing some sort of forged metal ring that he imbued with his own essence in order to exert some kind of magical control over the elves to subdue them is ridiculous from the beginning. By definition, he already had that power and more. What's more, Tolkien made clear in his own "rulebook" establishing the Valar and Maiar in The Silmarillion that only God Himself had the power to "create something out of nothing." Following that logic, Sauron could not have given the Ring more power than he already had within himself, so the very idea of the need for the Ring in the first place fails a test of logic even within Tolkien's own rules. Nothing about the Ring could amount to more than the sum of Sauron's own being, so what could he possibly have gained by making a Ring? And then to go from being essentially indestructible and unassailable by his very nature as a Maia, to making the Ring and letting a significant part of his own essence and power become part of such an obvious "single-point failure" device that all his enemies would immediately understand and attack as the one way Sauron could be destroyed? When that wasn't even necessary? From a military standpoint, even a drooling idiot could see that wasn't exactly Sauron's moment of shining brilliance in his strategic planning to take over the world. On the contrary, it makes him out to be a total moron on the level of a half-witted caveman, as opposed to what he was supposed to be in Tolkien's world: one of the first lieutenants of Morgoth, an accomplished, subtle, sophisticated military genius.
The Ring is a plot point where you sort of have to exert a suspension of disbelief within the original suspension of disbelief that you need to read any kind of fantasy to begin with. In other words, the Ring itself is a deus ex machina even within the rulebook of the fantasy world Tolkien created. You just have to accept it for how Tolkien wrote it, because there is no real adequate explanation for its existence that conforms to the "science" of Tolkien's world. Tolkien was a terrible writer from the standpoint of overusing deus ex machina. He used this "get out of jail free" card in numerous episodes of all his works. For example, the overuse of the eagles comes to mind. Shadowfax is another. The Paths of the Dead. And so on.
So ironically, the very premise of the Ring itself is one of the weakest plot devices in the entire story. There is no logical or satisfactory answer to why it even needed to exist in the first place. You just have to enjoy the story for what it is and accept the Ring as part of the story without delving too deep into the "science" behind it, because it fails pretty fast when you start thinking too deep about it.
Edit for comments:
You guys are missing the point entirely. I love Tolkien's stories, I re-read them about once a year. But the OP was asking for logical answers to questions that cannot really bear much scrutiny, and was treading on a plot point of the story that is among the thinnest ice on that lake. High fantasy stories like LOTR fall completely apart beyond just a couple levels of "why?" questions unless they are extremely well-crafted, and Tolkien's stories are not crafted very well much below the surface, that's just the literary truth of the matter. Luthien should not have had any chance of overcoming Sauron. Elendil and Gil-Galad shouldn't have had any hope of overcoming Sauron, who was in Tolkien's universe a Maia (and a very powerful one at that, one of Morgoth's most important and powerful lieutenants), an angelic being of infinitely greater power and strength than a mere mortal man or a flesh-and-blood Elf. The very idea is nonsense even within Tolkien's own universe.
As to the Ring "enhancing" Sauron's power, how could Sauron's power be enhanced by something that could only contain his own original power to begin with? Enhancing his power means he's gaining something he didn't already have. But Tolkien's own explanations of the Ring said that Sauron let a great deal of his own power pass into it. So it doesn't contain anything within itself that he didn't already have to begin with, so what again was the entire point to the Ring in the first place? Again, such a question is circular nonsense, it's like you're trying to make some kind of logical sense out of unraveling a Moibus strip.
Stories like these have to be simply enjoyed for what they are. Tolkien created a rich, detailed world for us to walk around in and admire. But I think what happens sometimes is that when an author creates a world that is so rich as Tolkien's, we lose a sense that we're just reading a story and start trying to take that world apart piece by piece just like the curious humans that we are. We don't just like the beautiful watch, we want to take it apart and see what makes it tick. That works in our reality because it's real; when you start taking apart someone's made-up world, though, the whole story quickly falls apart. The OP's very questions make that clear: the obvious answer is that Sauron wouldn't have needed a Ring in the first place.