To answer the only directly and objectively answerable question, Tolkien seems never to have discussed "this strange state of affairs" in his letters.
That said, I believe you're misremembering and misinterpreting parts of the book. To go through your various points more or less in sequence:
Elves of Mirkwood and Lórien
Legolas does state that the Elves of Mirkwood have not visited Lórien for a long time, but he doesn't state that they "don't even know if they are still there." Instead his comment is
We hear that Lórien is not yet deserted. ... Nevertheless its folk are seldom seen.
The lack of communication between the two kingdoms is easily explained, though: Mirkwood was much more concerned with its neighbors to the east and northeast, with whom it had longstanding trade agreements, than with its neighbor to the southeast which was largely pursuing an isolationist policy.
Erebor and Moria
Again I think you're misremembering something here. Gimli makes a comment while the Fellowship is in Moria to the effect that he's now unsure that Balin ever came there. It is Frodo, not Gimli, who states (on seeing Balin's tomb) "He is dead then ... I feared it was so." (Fellowship of the Ring, Book II, Chapter 4, "A Journey in the Dark")
Gimli's father Glóin states during the Council of Elrond that for a while Erebor had occasional messages out of Moria, all with good news; then the messages stopped. No one, in fact, says that "his people knew that something terrible had happened." One could speculate that the dwarves concluded that no news was good news, or alternatively that Daín was indeed concerned, but that as a king he could not justify sending a rescue expedition. We are not told what he thought; or on what basis, assuming he did consider a rescue mission, he might have turned down the idea; or what his emotions surrounding any such decision might have been.
Either way, I don't see textual evidence supporting the idea that the dwarves of Erebor, individually or collectively, felt little or no affection for their friends, acquaintances, and compatriots in Moria.
Bilbo's party and the aftermath
You state that
Bilbo seems to have few reservations about walking away from most of the people he was closest to for most of his life
But in fact, we're told that
he had no close friends, until some of his younger cousins began to grow up
He seems to have been in fact tolerated rather than liked by his family and his neighbors. He was "on visiting terms with his relatives", we hear, but it seems no more than that.
The only real friend he seems to have had was Frodo; and he was very concerned about leaving him. As for "messing with their minds" by disappearing, the narrator tells us that people take it as a joke. One in very poor taste, but a joke nevertheless—to which people respond with indignant surprise, but not (generally speaking) with anger or by taking offense. We're told:
It was generally agreed that the joke was in very bad taste.
Even the Tooks (with a few exceptions) thought Bilbo's behaviour was absurd.
For the moment most of them [them ambiguous between the Tooks and the hobbits generally] took it for granted that his disappearance was nothing more than a ridiculous prank.
Most of the guests went on eating and drinking and discussing Bilbo Baggins' oddities, past and present.
It's only the Sackville-Bagginses who appear to take umbrage or be offended; but they seem to take offense at Bilbo and Frodo generally. I see no evidence in the text that (after the initial shock) Bilbo's guests feel upset or offended by his actions.
Some of the gifts he leaves behind (all indeed labeled) do have "some point, or some joke", as the narrator says; but we're also told that
most of the things were given where they would be most wanted and most welcome. The poorer hobbits... did very well.
As far as the labels with a "point" or "joke", the one to Lobelia was definitely sarcasm. The others, though, seem no more than gentle irony pointed at some well-known characteristic, or flaw. Adelard Took was well-known for borrowing umbrellas, and Hugo Bracegirdle for borrowing books. Milo Burrows was well-known for not answering letters, and Dora Baggins for answering them. I see no evidence there of any specific "slight" against Bilbo himself, and no reason to believe that Bilbo is here exhibiting any lack of concern for friends or relatives.
(all quotes in this section from The Fellowship of the Ring, Book I, Chapter 1, "A Long-Expected Party")
Théoden and Gríma
Surely people close to Théoden do see what's happening to him;but what are they going to do? Kill Gríma and be executed for murdering one of the King's councillors? There's not a whole lot that can be done here; and remember that obedience to the king is the usual and ordinary way of showing love for him.
Théoden was in no sense enspelled. Gandalf, who above all people should know, describes Théoden as being influenced by "Wormtongue's whispering", and describes Wormtongue as "dulling men's wariness ... working on their fears", "urging" and "persuading" Théoden—not the sort of language that might be expected of one who had his subject under a spell. Gandalf specifically says, indeed, that before he escaped from Orthanc to warn Théoden
others watched and could do nothing, for your will was in his keeping.
(The Two Towers, Book III, Chapter 6, "The King of the Golden Hall")
There's no evidence that I see, then, that those around Théoden didn't love or care for him (and there's the evidence of Éowyn to set against that hypothesis). There is, however, the evidence cited above to support the thesis that those around him loved and cared for him, but were (as Gandalf states) at a loss how to act so as to both counter Wormtongue and simultaneously continue to appear loyal subjects. Éomer tried to do this and failed.
Aragorn and Arwen
It may seem surprising that Elrond apparently never mentions his daughter to Aragorn (who is not precisely being raised "as [Elrond's] own son"; we're merely told that Elrond "came to love him as a son of his own"). But then, we don't know what casual conversation among elves looks like. We never get any.
Regardless, it would be premature at best to conclude that Elrond displays any sort of "lack of interest" in his daughter. Indeed, the one of the main reasons he tells Aragorn to lay off talking to her is because he doesn't want the doom of mortality to come between them:
Then suddenly the foresight of [Aragorn's] kindred came to him, and he said: "But lo! Master Elrond, the years of your abiding run short at last, and the choice must soon be laid on your children, to part either with you or with Middle-earth."
"Truly," said Elrond. "Soon, as we account it, though many years of Men must still pass. But there will be no choice before Arwen, my beloved, unless you, Aragorn, Arathorn's son, come between us and bring one of us, you or me, to a bitter parting beyond the end of the world. You do not know yet what you desire of me."
(The Return of the King, Appendix A (I) (v), "[A Part Of] The Tale of Aragorn and Arwen")
This hardly sounds like the voice of someone who doesn't feel any interest in or concern for his child.
Again, when the time for their parting finally arrives, we're told that
Arwen Evenstar remained [at Edoras] also, and she said farewell to her brethren. None saw her last meeting with Elrond her father, for they went up into the hills and there spoke long together, and bitter was their parting that should endure beyond the ends of the world.
(The Return of the King, Book VI, Chapter 6, "Many Partings")
It is quite clear from this that Arwen and her father care deeply for one another. Why Arwen's name never came up in conversation with Aragorn is unclear; no explanation is ever given in the text. But there's enough indication in the text of the emotional ties between Arwen and her father and brothers to make it clear that the lack has nothing to do with a lack of caring.
Beregond and Bergil
Beregond does allow his son to remain in Minas Tirith; so do some other families, with whose sons we see Bergil playing. Beregond himself does not "know full well that Sauron is about to...kill everyone inside"; in fact he says himself
Gondor shall not perish yet. Not though the walls be taken... There are still other fastnesses, and secret ways of escape into the mountains.
It doesn't seem to be the case that Beregond is unconcerned about his son's safety; but he does hold on to the belief that Minas Tirith will not be completely destroyed.
Faramir and Denethor
The people of Gondor as a whole do love Faramir, true; but it is not the people as a whole who are involved with Denethor's last hours, they are Denethor's personal servants. In light, for example, of the oath the Guards (including Pippin) are required to take, it's clear that obedience is a prime requirement for them; and they may be too used to obeying orders, and too scared, to do anything but what their master asks.
Much of this answer, I realize, could be counted as "opinion-based"; but I hope to have shown that it's not necessarily, and certainly not clearly, the case that "people seem to display a shocking lack of affection and interest in their friends, family, and acquaintances."