[denethorthefirst]

denethorthefirst is quite right about at least some of the Dwarves participating in the War of the Last Alliance against Sauron. I had forgotten the mentions in Unfinished Tales. *My shame*

But I still disagree with denethorthefirst’s narrow definition:
The only function of the One Ring was to dominate (the bearers of) the other Rings of Power and to somehow enhance Saurons ability to dominate other wills.
My listing of various powers and abilities shown by the One Ring was to indicate that the One Rings shows powers not covered by this “narrow definition”.

I do not see that Sam’s listening in on the Orcs telepathically enables either Sam or Sauron to dominate the wills of those Orcs. The Orcs are not even bearers of other Rings of Power.

Throughout The Lord of the Rings we see several characters tempted to control the Ring, but no-one tempted by an increased desire to submit himself or herself to Sauron’s will. Gollum, Bilbo, Frodo, Galadriel, Boromir, Saruman, and even Sam, are tempted to take the Ring for themselves, to use against Sauron, which is surely not Sauron’s will. (Unless you wish to suggest that Sauron is transmitting a suggestion to the bearer of the One Ring to reveal himself [or herself] as a trick, as Sauron expected to quickly overcome whoever now had the Ring, once that was revealed. That would be possible in some cases, but not in most.)

Nor is their even a hint, I believe, that Sauron was using his will through the One Ring especially to defeat either Elendil or Isildur in the War of the Last Alliance. Isildur is in the end overcome by his desire for the One Ring itself, when Isildur first names it his “precious”.

You seem to be misunderstanding or misreading what i wrote!

I already explained it:
The "narrow" definition states that the only (intended by Sauron when he forged it) powers of the one Ring are:
1. It allowed the bearer (Sauron at the time) to directly dominate the other Rings of Power (and their bearers) and
2. it also enhanced the bearers (Sauron at the time) ability to "intrude"/"read" (osanwe) and dominate other (non-ringbearer) wills (i.e. made it easier for him to break the barriers of unwill of persons that weren't wearing other rings of powers).
I dont like this definition (I favor the "broad" view of the Rings Powers), but it is completely supported by Tolkien!
These two functions of the One Ring are the ONLY directly mentioned powers of it (and all the powers you listed are covered by this "narrow" definition!)!

But: Sauron could only perform those two functions of the One Ring when he was in possession/control of it! (I think thats quite obvious! Thats why he wasn't able to dominate the other Rings of Power in the Third Age and the Elves were free to use their Three Rings in safety) He cant work through or control the One Ring from a distance, but he is still "connected" to his power within it and he is not "diminished" because of the loss of the One Ring (Letter 131).
Sauron is clearly not almighty: there are of course a lot of people in Middle-earth that are completely independent from him. For a lot of those the One Ring is tempting: it fills the mind of others with delusions of grandeur (Boromir, Galadriel, even Sam!). But i think that was an unintended side-effect of the One Ring: the Power that Sauron put in the Ring was so great that it had a "seducing" effect on lesser beings. I dont think thats something Sauron intended: he probably never thought he would lose it!

I NEVER wrote that the second function of the One Ring (the ability to more easily read/dominate other minds) worked only with other ring-bearers!
Sam, even though he is not trained, is able, when he is wearing the One Ring (and according to his own innate power), to "intrude"/"read" the mind of weaker wills (the orcs).
Tolkien also wrote in a letter that it was the One Ring that helped Sauron to easier dominate and manipulate the Numenoreans (almost an entire people!).
Other people besides Sauron could use the Ring, according to their own innate Power, even if they are not able to completely master it. For example: while Sam is able to access a tiny part of the Rings Power with respect to the lesser Orcs, he couldn't dominate the Three Ringbearers (Gandalf, Galadriel, Elrond) and he would surely fail if he tried, with the help of the One Ring, to break the barriers of unwill of a more powerful non-ringbearer (like for example Denethor II).

Nor is their even a hint, I believe, that Sauron was using his will through the One Ring especially to defeat either Elendil or Isildur in the War of the Last Alliance. Isildur is in the end overcome by his desire for the One Ring itself, when Isildur first names it his “precious”.

Of course Sauron used the One Ring in the War of the last Alliance, but Gil-Galad, Isildur, and especially Elendil were exceptional beings that had a lot of willpower and they resisted his efforts - i never wrote that the One Ring was somehow almighty. It allowed Sauron to better break the barriers of unwill and dominate/intrude other minds, but even while he was successfully doing that during his stay in Numenor, at least some (the Faithful) were resisting him!
We also have to take into account that the actual direct contact Elendil, Isildur and Gil-Galad had with Sauron was limited - and they resisted him successfully during that limited time! They might not have been able to resist his willpower for a prolonged period of time if, for example, Sauron had captured and (mentally) tortured them.

Note some readers find it odd that the One Ring is not even mentioned in the accounts of the Fall of Númenor save when the spirit of Sauron takes up again his great Ring in Barad-dûr after the drowning of Númenor. Had the One Ring not been with Sauron at all during his captivity in Númenor but hidden in Barad-dûr? Well, at least in Letter 211 of Letters of J. R. R. Tolkien, Tolkien wrote:
Though reduced to ‘a spirit of hatred borne on a dark wind’, I do not think one need boggle at this spirit carrying off the One Ring, upon which his power of dominating minds now largely depended.
So this tells us that in this time and place Tolkien imagines that Sauron, without the One Ring, would have little special power to persuade, as perhaps we should imagine him at the end of the Third Age. Yet Sauron has somehow persuaded hoards of Easterlings and Southrons to join him. Presumably we are to imagine that much of the power that he had put into the One Ring had returned to him.

Of course Sauron had the One Ring with him in Numenor (Tolkien himself says so), it was a part of him and he would never separate willingly from it.
You're wondering why Sauron is able, without the One Ring, to command Easterlings and Southrons. Sauron was simply manipulating them (like any sly politician would). We have to remember that those people are on a rather primitive cultural level; i think it was relatively easy for Sauron to manipulate them into thinking that he was some kind of God. He also laid the Groundwork and Foundation of his Third Age Rule in the Second Age (when he had the Ring).
But the notion that Sauron somehow transferred (or "got back") large parts of his power from the One Ring during the Third Age (even though he wasnt in posession???) is completely "un-tolkien" and not supported by the text!