Did they all leave? If not, who didn't?
The Ringbearers left quickly -- Elrond, Galadriel -- and I think the remaining High Elves mostly left in the first few years of the Fourth Age.
Celeborn established a new realm of Lůrien, the southern half of Mirkwood, sharing it with the Woodmen in the middle and Thranduil on the north side. This the ancient friction between Lůrien and the Woodland Realm was healed (after Galadriel left; I'm sure that helped).
:"Some there are among us who sing that the Shadow will draw back, and peace shall come again. Yet I do not believe that the world about us will ever be as it was of old, or the light of the Sun as it was aforetime. For the Elves, I fear, it will prove at best a truce, in which they may pass to the Sea unhindered and leave Middle-Earth for ever." ~Haldir
Haldir has made up his mind to sail, well aware that Nenya would not hold Lůrien under its spell much longer. It seems from the Tale of Aragorn and Arwen in the Appendix that Lůrien was utterly abandoned by the end of Elessar's reign.
From the foreward of FOTR we hear that Celeborn soon moved to Imladris with Elrond's sons and "some of the High-elven folk" but that when Celeborn left, he took with him "the last living memory of the Elder Days in Middle-Earth." That implies Cirdan went with him, if not before.
And now I see I've missed something, if we take that statement as authoritative (Tolkien occasionally makes blanket statements without considering all the ramifications, just as we do).
I knew that meant all the High-Elves left before Celeborn. But it seems to imply Thranduil also left. I am not 100% sure he was born in Doriath, before his father left it, but I think so. Somehow I thought he'd be immune from the call of the Sea, since he never went near it, and that, ironically, the SIndar who had rejected Valinor and the Exiles would be the last reigning Elvenking on Middle-earth, ruling over a primitive people like the Elves in the earliest days before the sun and moon, until they "forgot and were forgotten". But apparently even Thranduil gave in and went to Valinor, in spite of ancient misgivings. It was still, I suppose, better than living in the world of Men.
:He suspects, but he does not know - not yet. Do you not see now that your coming to us is as the footstep of Doom? For if you fail, then we are laid bare to the Enemy. Yet if you succeed, then our power is diminished, and Lothlůrien will fade, and the tides of Time will sweep it away. We must depart into the West, or dwindle to a rustic folk of dell and cave, slowly to forget and be forgotten. ~ Galadriel
I always imagined she was referring to the Wood-elves and any other of the Teleri who were not willing to forsake Middle-Earth. It is an interesting comment, because she is describing the style of elves, nymphs, fairies, and leprachauns that are rife in Victorian literature, ennobled somewhat by Tolkien's mentor George MacDonald, and which Tolkien himself was writing when he first started his mental journey to Middle-Earth. His earliest writing makes Melian a Faerie Queen, Tiniviel is a little dancing fairy-like creature, and even the Wood-elves of The Hobbit are not as mature as his Eldar in LOTR. Basically Galadriel's prediction is epexegetical to explain why modern legends of elves make them a "rustic folk of dell and cave." Elves will fade, if they stay any longer in the mortal world in the Fourth Age. That is her warning.
Elladan and Elrohir were not of the Elder Days, but younger, and stayed after their father hand gone. No doubt they were not satisfied while any orcs, the tormentors of their mother, were left in the world. But did they stay too long? I thought I had read somewhere that a doom was put on Elrond, that when he left Middle-earth, all his children must then make their choice to go or stay, and if they stayed, they were mortal. Did Elladan and Elrohir choose to commit themselves to Middle-Earth where they were born?
And what of other Elves?
Legolas took some to Ithilien. Did they leave before him? Did any choose to stay and meet the doom Galadriel describes? He evidently outstayed Cirdan, for he built his own ship. Arwen, at the same time, told Elessar on his deathbed that no ship remained to bear her West, whether she wished to renounce the Doom of Men or not. Surely she assumed that because Cirdan was gone, and it had not occurred to her another Shipwright was left in Middle-Earth.
I have always wondered whether it would have been better or worse for her to know Legolas had a means for her, if she had the will.
She went looking for Celeborn. I keep wondering whether she was simply seeking her grandfather, whom she guessed to be the last to leave Middle-Earth, or whether she was hoping to go with him. The ending of the Tale of Arwen and Aragorn is very unclear about whether she repented her choice in the end, but felt she had no choice left.
I still come back to this: did Legolas and Gimli take the last elves in Middle-earth with them? Somehow from the description of their departure I imagined it was just the two of them, alone. Or did some Wood-elves, some of the younger Elves of the Second and Third Age who did not remember Elder Days, choose to dwindle rather than lose what little they had left?
They all would have left eventually, this being the main reason why Tolkien abandoned 'The New Shadow', a story set in the fourth age, centred around Gondor. Without the presence of the Elves, there was no real element of Fantasy, rendering the story useless. I only just got up, and don't feel in the mood to research inot your individual questions. Maybe someone else can.