To answer this, first of all I'm going to divide the Rings into groups, slightly different to those you've chosen. These groups are:
- The One Ring, obviously.
- The Three Elven Rings, which were made separately, last of all, by Celebrimbor alone, but yet also subject to the One.
- 16 Rings, comprising the Seven and the Nine. These go together because Tolkien never actually ascribes different capabilities to them; their effect is a function of the species that uses them rather than of anything particular about the Rings themselves.
- The other lesser rings mentioned by Gandalf in Shadow of the Past - "only essays in
the craft before it was full-grown, and to the Elven-smiths they were but trifles" - which I'm going to ignore.
Now let's look at something interesting: we can establish that being in possession of, but not actually wearing, a Ring is sufficient to remain "hidden"; the Elves only become aware of Sauron when he puts on the One Ring
As soon as Sauron set the One Ring upon his finger they were aware of him; and they knew him, and perceived that he would be master of them, and of all that they wrought.
...and that Sauron cannot determine where the Three are, nor control them, when they're not being worn (and crucially also: not used openly):
Then in anger and fear they took off their rings ..... Sauron could not discover them, for they were given into the hands of the Wise, who concealed them and never again used them openly while Sauron kept the Ruling Ring.
The latter also means: it's safe to wear, and even to use, one of the Three so long as you're discreet about it, and this applies even if someone is possessing or even wearing the One.
Moving on some more, let's look at the Ring inscription:
One Ring to rule them all, One Ring to find them
One Ring to bring them all, and in the darkness bind them
The intention here is clear: the only Ring that gives dominance over any of the others is the One - otherwise Tolkien would have written something like "20 Rings each of which rules/finds/brings/binds the other 19".
So the only situation where awareness/etc occurs is where one of the parties, X or Y, is wearing the One Ring. Also, because in the Rings of Power quote Tolkien does not specify which Rings the Elves were wearing (and took off) we must assume that awareness/etc occurs equally for the Three and the Sixteen.
Finally, the specific power of the One over the others (Nineteen) is given as (Rings of Power, again):
...while he wore the One Ring he could perceive all the things that were done by means of the lesser rings, and he could see and govern the very thoughts of those that wore them.
(Again note the condition that the Rings must be worn, and not merely possessed.)
Now we can attempt some answers.
Answer 1 : Is X 'aware' of the existence of Y?
Not necessarily; the only combinations where X is aware of Y are:
- X is wearing the One Ring.
- Y is wearing one of the Three or the Sixteen.
- Y is using their Ring and is not being discreet about it.
- X is wearing one of the Three or the Sixteen.
- Y is wearing the One Ring.
(There's an obvious exception to these which I'll come to at the end)
Answer 2 : Does X know that the state of use of Ring RY
I'm taking this one next because it's tied with the first answer. We've established already that both X and Y must be wearing their Rings for even the most basic awareness to occur, so the answer is:
- Yes, but,
- because both RX and RY must both be worn,
- and assuming that if the first combination applies, the full combination is satisfied,
- the state will always be: "it's being worn",
- but don't forget that one of RX and RY must be the One (it doesn't matter which).
Answer 3 : How much information can X obtain about Y in this situation?
Here we need to look again at the Rings of Power extracts.
For the first combination (in Answer 1, above) it's almost total dominance; taking Sauron as X (wearing the One) and the Elves as Y (wearing one of the Three or the Sixteen):
- what Y is doing with RY,
- what Y is thinking,
- where Y is (because "Sauron could not discover them" after the Elves took off the Rings),
- when Y takes off RY (obvious, because again "Sauron could not discover them"),
- but remember that Y can be discreet and remain undiscovered.
For the second combination it's simpler; where the Elves were X (wearing one of the Three or the Sixteen) and Sauron was Y (wearing the One):
- they were aware of him,
- they knew him (presumably not Biblically),
- they perceived that he would be master of them,
- and of all that they wrought.
So the information that X can obtain about Y here is:
- that Y exists,
- who Y is, even behind any disguises (because Sauron was operating in his Annatar form at the time),
- what Y's motives towards X are.
Answer 4 : Can X communicate proper specific information/emotions to Y?
I'm taking these two together, and although I suspect that the answer is probably obvious from the above, I'll discuss it some anyway.
Recalling that one of RX or RY must be the One Ring, and that it doesn't matter whether the other is one of the Three or the Sixteen, the answer is:
- No, but,
- the holder of the One can read the thoughts of the other, and,
- limited reading of knowledge of motives, etc is possible in the other direction.
So it's not a case of "communication to", but "reading from", and more limited in one direction than the other, depending on which of X or Y is holding the One.
I mentioned an exception to the "awareness" answer above, and this is obviously when Frodo sees Galadriel's Ring in Lothlorien, but Sam doesn't. Frodo, of course, is not actually wearing the One at the time. First of all Frodo asks (and note again the condition of wearing):
I am permitted to wear the One Ring: why cannot I see all the others and know the thoughts of those that wear them?
And Galadriel herself provides the answer to this:
You have not tried. Only thrice have you set the Ring upon your finger since you knew what you possessed. Do not try! It would destroy you. Did not Gandalf tell you that the Rings give power according to the measure of each possessor? Before you could use that power you would need to become far stronger, and to train your will to the domination of others. Yet even so, as Ring-bearer and as one that has borne it on finger and seen that which is hidden, your sight is grown keener.
There are also cases where Sauron is aware of Frodo while Frodo is wearing the One, as is Gandalf ("Take it off! Take it off! Fool, take it off!")
Galadriel's answer also answers for Sauron: he too was a Ring-bearer, he bore it on his finger, he has also seen that which is hidden: his sight has also grown keener. But yet not that keen.
The three times Frodo wears the Ring that she mentions are:
- In Bombadil's house,
- in the Prancing Pony,
- on Weathertop.
In none of these cases is there any evidence of the Eye - the First time Frodo sees that is in the Mirror of Galadriel.
Subsequently he wears the Ring on Amon Hen, and we see that:
Then at last his gaze was held: wall upon wall, battlement upon battlement, black, immeasurably strong, mountain of iron, gate of steel, tower of adamant, he saw it: Barad-dûr, Fortress of Sauron. All hope left him.
And suddenly he felt the Eye. There was an eye in the Dark Tower that did not sleep. He knew that it had become aware of his gaze. A fierce eager will was there. It leaped towards him; almost like a finger he felt it, searching for him.
This is clear: Sauron only becomes aware of Frodo after Frodo has his vision of Barad-dûr, so Frodo must be actually looking at Sauron for Sauron to have this awareness: that's when Sauron's vision becomes keen.
Unfortunately I'm unable to give a satisfactory explanation of Gandalf's awareness; it may be because he's wearing his own Ring at the time (and is therefore aware of Frodo wearing the One) or it may be just Maia-powers in operation. There's nothing to say that neither could be the case, and it seems weak to finish on this note, but I've already made this a lot longer than I'd intended, so I'll stop roundabout now.