Shh, I'm here too

In my opinion, Faramir (or Denethor, Aragorn, etc) doesn't necessarily read thoughts like a book, particularly not with a mind as resistant as Gollum's. Faramir describes Gollum's mind in particular as dark and closed, it seems unusually so—

"There are locked doors and closed windows in your mind, and dark rooms behind them," said Faramir.

Still, Gollum is unable to entirely block Faramir's abilities. In LOTR, it does not seem that Gollum can fully block powerful mental abilities such as Faramir's, though his toughness and hostility does limit what Faramir can see. (Unfinished Tales, incidentally, suggests iirc that Denethor's combination of "great mental powers" and his right to use the Anor-stone allowed him to telepathically get the better of Saruman through their palantíri, a similar but greater feat.) I imagine that this is roughly similar to, but scaled down from, Galadriel's telepathic inquiries of even someone as reluctant to have her in his mind as Boromir, given that Faramir is able to still see some things in Gollum's mind, if with more difficulty than usual.

(WRT Boromir ... ngl, if I was the human buffer between Denethor and Faramir, I would also not be thrilled about sudden telepathic intrusions from basically anyone, much less someone I had little reason to trust.)

Disclaimer: a few years after LOTR's publication, Tolkien tried to systematize how this vague mystical telepathy stuff really works. One idea he had among many, iirc, was that no unwilling person's mind could be "read" the ways that Gollum's is throughout LOTR. IMO that can't really be reconciled w/ numerous significant interactions in LOTR where resistance to mental intrusion or domination is clearly variable between individuals and affected by personal qualities like strength of will, basic resilience, the effort put into opposition, supernatural powers, etc. And these attempts at resistance are unsuccessful or only partially successful on many occasions in LOTR (the Mouth of Sauron, for one example, is a Númenórean sorcerer in the book who can't really contend with Aragorn on a telepathic level). So I, personally, tend to avoid using the terminology and rationales from that later systematized explanation when discussing LOTR. And in general, I think Tolkien's later attempts to convert the mystical, mysterious wonder of Middle-earth into something more "hard magic" or even scientific was a failed idea on a par with Teleporno. Others differ!

In any case, when Gollum "unwillingly" looks at Faramir while being questioned, the creepy light drains from his eyes and he shrinks back while Faramir concludes he's being honest on that specific occasion. Gollum experiences physical pain when he does try to lie to Faramir—

"It is called Cirith Ungol." Gollum hissed sharply and began muttering to himself. "Is not that its name?" said Faramir turning to him. "No!" said Gollum, and then he squealed, as if something had stabbed him.

I don't think this is a deliberate punishment from Faramir—that wouldn't be like him at all—and I don't think it's the Ring, but simply a natural consequence of what Faramir is. Later, Gandalf says of Faramir's father:

"He can perceive, if he bends his will thither, much of what is passing in the minds of men ... It is difficult to deceive him, and dangerous to try."

So, IMO, Faramir's quick realization that Gollum is a murderer doesn't come from any vision of the future or past involving Gollum—that is, it's not a deduction from some event he's seen. Faramir does not literally foresee Gollum's trick at Cirith Ungol. His warning would be more specific in that case, I think. What he sees seems to be less detailed but more direct and, well, mystical. Faramir likely doesn't know who exactly Gollum murdered or why or what any of the circumstances were. Rather, Gollum's murderousness and malice are visible conditions of his soul to Faramir's sight. Faramir doesn't foresee the particulars of Gollum's betrayal—but he can see in Gollum's mind that he is keeping something back. Faramir says of Gollum:

"I do not think you are holden to go to Cirith Ungol, of which he has told you less than he knows. That much I perceived clearly in his mind."

Meanwhile, in a letter written shortly before the publication of LOTR, Tolkien said of Faramir's ancestors:

They became thus in appearance, and even in powers of mind, hardly distinguishable from the Elves

So these abilities aren't that strange in that context. Faramir by chance (or "chance") is, like his father, almost purely an ancient Númenórean type despite living millennia after the destruction of Númenor (that destruction is the main reason "Númenóreanness" is fading throughout the age Faramir lives in). Even less ultra-Númenórean members of Denethor's family are still consistently inheriting characteristics from their distant ancestor Elros, Elrond's brother, while Faramir and Denethor independently strike Sam and Pippin as peculiarly akin to Gandalf, a literal Maia like their ancestress Melian:

“Ah well, sir,” said Sam, “you [Faramir] said my master had an elvish air; and that was good and true. But I can say this: you have an air too, sir, that reminds me of, of—well, Gandalf, of wizards.”

He [Denethor] turned his dark eyes on Gandalf, and now Pippin saw a likeness between the two, and he felt the strain between them, almost as if he saw a line of smouldering fire drawn from eye to eye, that might suddenly burst into flame.

Meanwhile, Faramir's mother's family is believed to be part Elvish, a belief immediately confirmed when Legolas meets Faramir's maternal uncle:

At length they came to the Prince Imrahil, and Legolas looked at him and bowed low; for he saw that here indeed was one who had elven-blood in his veins. "Hail, lord!" he [Legolas] said. "It is long since the people of Nimrodel left the woodlands of Lórien, and yet still one may see that not all sailed from Amroth’s haven west over water."

In addition to that, Faramir's men believe he's under some specific personal blessing or charm as well as the Númenórean/Elvish/Maia throwback qualities. It's also mentioned by different groups of soldiers that Faramir can exercise some power of command over animals as well as people. Beregond describes Faramir getting his horse to run towards five Nazgûl in real time:

"They will make the Gate. No! the horses are running mad. Look! the men are thrown; they are running on foot. No, one is still up, but he rides back to the others. That will be the Captain [Faramir]: he can master both beasts and men."

Then, during the later retreat of Faramir's men across the Pelennor:

At last, less than a mile from the City, a more ordered mass of men came into view, marching not running, still holding together. The watchers held their breath. "Faramir must be there," they said. "He can govern man and beast."

Tolkien said of the ancient Númenóreans:

But nearly all women could ride horses, treating them honourably, and housing them more nobly than any other of their domestic animals. The stables of a great man were often as large and as fair to look upon as his own house. Both men and women rode horses for pleasure … and in ceremony of state both men and women of rank, even queens, would ride, on horseback amid their escorts or retinues … The Númenóreans trained their horses to hear and understand calls (by voice or whistling) from great distances; and also, where there was great love between men or women and their favorite steeds, they could (or so it is said in ancient tales) summon them at need by their thought alone. So it was also with their dogs.

Likely the same Númenórean abilities were used for evil by Queen Berúthiel against her cats. In an interview with Daphne Castell, Tolkien said:

She [Berúthiel] was one of these people who loathe cats, but cats will jump on them and follow them about—you know how sometimes they pursue people who hate them? I have a friend like that. I’m afraid she took to torturing them for amusement, but she kept some and used them—trained them to go on evil errands by night, to spy on her enemies or terrify them.

The more formal version of the Berúthiel lore recurs in Unfinished Tales:

She had nine black cats and one white, her slaves, with whom she conversed, or read their memories, setting them to discover all the dark secrets of Gondor, so that she knew those things "that men wish most to keep hidden," setting the white cat to spy upon the black, and tormenting them.

Faramir, by contrast, has a strong aversion to harming/killing animals for any reason other than genuine need, but apparently quite similar basic abilities. He typically uses these abilities to try to compassionately understand other people or gather necessary information, rather than for domination or provoking fear. Even so, Faramir does seem to use his mental powers pretty much all the time with no attempt to conceal what he's doing—he says some pretty outlandish things to Frodo and Sam as if they're very ordinary, but it doesn't seem that most people he knows can do all these things. This stuff is ordinary to him because it flows out of his fundamental being, not because it's common.

It's not clear how much fine control he has, interestingly. This is more headcanon perhaps, but I don't feel like it's completely under his control, even while it's much more controlled than things like Faramir's vision of Boromir's funeral boat, his frequent, repeated dreams of Númenor's destruction, the Ring riddle dream he received multiple times, or even his suspiciously specific "guess" of what passed between Galadriel and Boromir in Lothlórien. Yet his more everyday mental powers do seem to involve some measure of deliberate effort in a lot of the instances we see, given the differing degrees of difficulty and strain we see with the powers he and Denethor exhibit more frequently and consistently.

This is is also interesting wrt Éowyn, because Tolkien describes Faramir's perception of her as "clear sight" (which I suspect is just Tolkien's preferred parlance for "clairvoyance"). Faramir perceives a lot more of what's going on with Éowyn than I think he had materially observable evidence for—but does not see everything that's going on with her by any means. He seems to understand basically everything about her feelings for Aragorn, more than Éowyn herself does, but does not know if she loves him [Faramir].

I'm guessing that it's more difficult to "see" this way when it's directly personal (one of the tragedies of his and Denethor's relationship is that their shared mental powers do not enable either to realize how much they love each other). But it also doesn't seem like he's trying to overcome Éowyn's mental resistance the way he was with Gollum, and possibly Frodo and Sam—he does handle it a bit differently when it's not a matter of critical military urgency. With Éowyn, he sees what his abilities make clear to him, is interested enough to seek out Merry (and also perceive more than Merry says, because Faramir has never been a normal person one day in his life) but doesn't seem to really push either of them.

So I tend to imagine that with someone like Faramir, Denethor, Aragorn etc, we're usually seeing a relatively passive, natural form of low-grade telepathy that simply derives from their fundamental nature and personalities (as we see in Faramir with Éowyn, possibly Faramir with Aragorn). That can be kicked up to more powerful, forceful telepathy via active exertion of the will (as described by Gandalf wrt Denethor's ability to "bend[] his will thither" to see what passes in others' minds, and seen with Faramir vs Gollum, Aragorn vs the Mouth of Sauron, more subtly Faramir vs Denethor). At a high point of strain this can be done very aggressively or defensively (Denethor vs Gandalf, Denethor vs Saruman, Denethor vs Sauron seriously is there a Maia that man won't fight, Faramir vs the Black Breath given his completely unique symptoms that Aragorn attributes to his "staunch will", possibly Aragorn vs the Black Breath in a healing capacity...).

Pharazôn cares about his ultimate supremacy as (in his view) basically god emperor over all humanity, but IIRC he has no interest in directly subjugating Elves or dwarves or whoever to his rule. He doesn't want non-human subjects, nor does he even care enough about them to be particularly interested in wiping them out. He didn't invade Aman in order to kill its Elves; he killed Elves because they were the way of his invasion. He, and the King's Men in general, are far from isolationists in any true sense, but their ideal world order is one in which they interact with other species as little as possible while having absolute eternal dominion over all of humanity. Anyone who gets in the way of any of those goals deserves, to him, to get ground up in the Númenórean war machine, but he doesn't think of them as already at war because there are Elves out there ruling Elves in places he has no real interest in. They only matter insofar as they're threats domestically or immediate obstacles to his empire.

And the prequels/sequels/whatever that work for me, the ones I can really love, are the ones that don't modify resolved character arcs that way. Lord of the Rings immeasurably expands on The Hobbit without suggesting that Bilbo's growth didn't really happen or that he'd need to keep repeating it for some reason. He's a minor presence in LOTR but he's very much the Bilbo from the end of The Hobbit, not the beginning.

My big fear with Rogue One is that it would sand my OT blorbo Anakin Skywalker down into generic fanboy one-dimensional Vader or he'd be much more ROTS-adjacent than OT-adjacent, without the mix of horror, menace, pathos, and occasional (terrifying) cringe that I think defines the character of the OT. Keeping Anakin to a few appearances without pushing his growth backwards or forwards for where he should be at that point, and including the quirks of his OT characterization ("don't choke on your aspirations" as an echo of "apology accepted..." <3), made it possible for me to also love Rogue One for its own sake and characters— there was no insistence that the arcs and resolutions of a completely different work that has been over for ages only seemed satisfying as a big fake-out in order to prop it up. It props itself up!

In fact, Rogue One draws on the conclusive, hopeful cohesion of the OT to underscore its own themes and arcs. When the injured Cassian asks if anyone heard and Jyn assures him someone did, we not only know from other scenes in the film that the Rebellion has heard, we've got the OT in the back of our heads, and the unbending commitment of the OT Rebellion to fighting the Empire. Rogue One doesn't say "maybe they aren't really," it says "maybe this is how they got that way." The very completeness of the OT is treated as a strength, not a problem.

This isn't an argument that Lucasfilm is The Good Franchise that doesn't pull the "lalala what arc" nonsense; it does the obnoxious franchise shit all the time. Rogue One specifically, though, steps carefully to avoid framing anything in the OT (or the prequels, for that matter) as incomplete, as any kind of fake-out that somehow needed Rogue One decades later to truly succeed as a story. Even the explanation for the fault in the Death Star design doesn't carry the sense of "this missing detail needed to be fixed" so much as an opportunity for storytelling that wouldn't disrupt the OT.