Technically, the "Last Ship" is the one which Cirdan and Celeborn take some time in the Fourth Age. It must be after year FoA 171, as a note in the Thain's Book - transcribed from the Red Book of Westmarch says that Cirdan might still live at the Grey Havens. Arwen also has the opportunity to depart after Aragorn's death in FoA 120.
Appendix A says that "grievous . . . was the parting of Elrond and Arwen, for they were sundered by the Sea and by a doom beyond the end of the world", that "Arwen became as a mortal woman", and finally that Arwen "laid herself to rest upon Cerin Amroth; and there is her green grave, until the world is changed".
You are correct that "At the Grey Havens dwelt Cirdan the Shipwright, and some say he dwells there still, until the Last Ship sets sail into the West." Appendix A also notes that "In the days of the Kings most of the High Elves that still lingered in Middle-earth dwelt with Cirdan or in the seaward lands of Lindon." But Appendix B says that "after the passing of Galadriel in a few years [after the War of the Ring] Celeborn grew weary of his realm and went to Imladris to dwell with the sons of Elrond." I can't find anything in Appendix B that talks about Celeborn taking ship, and I can't find this either in the section of Unfished Tales on Galadriel and Celeborn.
The only Fourth Age ships mentioned in Appendix are the one that took Sam, and then after the death of Aragorn the grey ship build by Legolas in Ithilien that carried him and Gimli "down Anduin and so over Sea".
See the note above regarding the date of the Last Ship. And the Gimli thing is definitely an "it is told" or an "if this be true" type thing; it is purposely placed in the region of speculation.
As is Cirdan's continued dwelling in the Havens.
the theme of exceptionalism is usually used purposely to illustrate deviation from what is normal, natural, the proper order of things and serves rather to strengthen the underlying motifs. This can be as the result of sorcery, the grace of the Valar, or Eru's personal intervention ("providence").
This may be so. It doesn't make the case for consistency, though. It's part of the case against it!
I think there's also a world of difference between "things we don't necessarily understand about Middle-Earth because they aren't made explicit" and "things which contradict established lore in Middle-Earth."
Well, the "established lore" is what has been written and published, and so in a sense it can't contradict itself: it is what it is. But "things we don't understand" (eg the relationship between, and timelines pertaining to, Galadriel and Celeborn) don't have some objective existence that we strive to uncover: there is no objective reality here that anchors our inquiry.
The fiction is written and our "understanding" flows from that. Consistency to prior "rules" or conceptions doesn't seem to be a particular constraint on JRRT's work.
These are functions of the corrupting influence of the Ring, and serve that motif.
As I posted upthread, the corruption could - considered in the abstract - manifest in any number of other ways, and from the point of view of setting consistency any would do as well as any other, and indeed
consistency might be increased if the Ring either made Gollum more like a Nazgul, or obliterated him with its power.
Bombadil might be Eru or the author inserting himself into the story; he is certainly an exception. Goldberry is a "not-known" but we might reasonably infer that she is a maia; Old Man Willow is consistent with the remains of the Primeval Forest, and the notion of "Ents becoming tree-ish/trees becoming ent-ish."
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Boromir's journey is exceptional.
Pointing out that certain things are exceptions or exceptional doesn't seem to me to
refute the case against consistency. It helps make it out.
There's an argument, in my view, that the whole of the Ent "arc" is an instance of this. Fangorn is full of these ancient peoples, and Celeborn and Galadriel live barely a stone's throw from them, and yet Treebeard (Bk VI, ch VI) laments that "It is long, long since we met by stock or by stone"; and earlier (Bk II, ch VIII) Celeborn warns the Fellowship not to "risk becoming entangled in the Forest of Fangorn. That is a strange land, and is now little known." Yet is seems that he and Galadriel know that Ents live there!
Again, illustrating the unnatural effects of sorcery.
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Well, the Witch-King, Galadriel and Sauron all "do magic," and I'm not sure that we're required to see the Mouth of Sauron do magic "on-screen" for his authenticity as a sorcerer to be confirmed.
But magic - and especially sorcery, the use of spells - is exactly whatever the story needs it to be, and no more. There is no consistent conception that I can see of what sorcery
is, or how it works, or what effect it can have. (This contrasts, for instance, with A Wizard of Earthsea.)
I'm not sure whether you're referring to the Palantir of Minas Tirith or in the Tower Hills.
The latter.