But whether they've been to Valinor before or not, all elves go there when they die, and all elves can leave Valinor and sail to the rest of Middle-earth if they want — though that hasn't happened particularly often in Tolkien's work, and when it has it's usually a big deal.
Once an Elf is granted passage from the Grey Havens to Valinor, they sail across the Sundering Seas and enter the Undying Lands, never to return to Middle-earth. Valinor is its own sort of heaven, an eternal land of paradise for Elves to live among the gods.
Valinor was located on the continent of Aman, far to the West of Middle-earth. It was the realm of the Valar and a place of bliss and perfection. In the deep past, travel between Valinor and Middle-earth was possible, but that ended in the Second Age.
Elves are already immortal and, therefore, can live forever in the Undying Lands in peace. The Men, Hobbits, and Dwarves of Lord of the Rings could live there, and they have, but when their time comes to see Mandos, their souls are moved into the mysterious afterlife for which Tolkien gives no description.
Although in the latest version of the story, Galadriel's story changed significantly, far from joining Fëanor's rebellion, she opposed him in nearly everything. And that she wished to leave Valinor and go to the vast world of Middle-earth, to give free rein there to her talents.
Why Are There No Elf Children in the Lord of the Rings?
Can Elves leave the Undying Lands?
But whether they've been to Valinor before or not, all elves go there when they die, and all elves can leave Valinor and sail to the rest of Middle-earth if they want — though that hasn't happened particularly often in Tolkien's work, and when it has it's usually a big deal.
Because it would have been a massive plot hole that breaks the logic of the story. The Valar are orders of magnitude more powerful than Sauron, even at full potential just after his fall into the influence of Melkor, or any force Sauron could control.
Men were never allowed to enter the Undying Lands after the fall of Numenor and any attempts to reach the lands would result in failure or disaster. Aragorn, despite his heroic deeds, likely wouldn't have accepted an invitation to ensure his duties as king.
This is all described by Tolkien in Letter 325: “As for Frodo or other mortals, they could only dwell in Aman for a limited time – whether brief or long. The Valar had neither the power nor the right to confer 'immortality' upon them.
The ship passed west upon the sea, and then took the hidden straight path to Valinor. Gandalf became Olórin once more. There, presumably, he dwells still in the gardens of Irmo.
The common perception is that Valinor is a kind of heaven for the inhabitants of Middle-earth (especially the Elves), a place they can go after a well-lived life. But, though Elves came from Valinor to fight against Morgoth, it was never actually their real home.
Elves are immortal but can be killed in battle, in which case they go to the Halls of Mandos in Aman. They may be restored by the Will of the Valar, and then go to live with the Valar in Valinor, like an Earthly Paradise, though just being in the place does not confer immortality.
Though Gimli has no children, he is not the last Dwarf of Middle-earth. After the fall of Sauron, his people continued to thrive in the Lonely Mountain. Gimli made his home in Rohan, in the Glittering Caves of Aglarond, and many of his kinsfolk came with him.
All those Elves who never reached Valinor are "Dark Elves." In the First Age, the Sindar viewed the term "Moriquendi" as offensive, so the Noldorin Exiles gave the name Úmanyar ("Those not of Aman") to those who started the journey but did not finish it.
Legolas does not marry or have any children, based on the appendix of The Lord of the Rings. Regardless of who his mother was, Legolas is the last of his line. When he sails into the West at the beginning of the Fourth Age, he leaves no family members behind.
Elves are immortal but can be killed in battle, in which case they go to the Halls of Mandos in Aman for an afterlife. They may be restored by the Will of the Valar, and then go to live with the Valar in Valinor, like an Earthly Paradise, though just being in the place does not confer immortality, as Men supposed.
By the Time of The Lord of the Rings, Galadriel Is Over 8000 Years Old. With Galadriel being born in YT 1362, that means she lived for 138 years in Valinor, as the Years of the Trees ended in 1500. So, her 138 years, multiplied by 9.582, places Galadriel at 1322 years old when the First Age of Middle-earth began.
As far as mortality, no. Mortals don't gain immortality in Valinor. In fact, being there speeds up their deaths, which is one of the reasons mortals are banned from entering.
Arwen reciprocated Aragorn's love, and on the mound of Cerin Amroth they committed themselves to marrying each other. In making that choice, Arwen gave up the Elvish immortality available to her as a daughter of Elrond, and agreed to remain in Middle-earth instead of travelling to the Undying Lands.
After Morgoth's defeat at the end of the First Age, elves like Galadriel were pardoned and offered a return to the land they abandoned. Galadriel refused, partly because she believed her people had no reason to need pardoning, but more because she always wanted to witness Middle-earth and rule a kingdom there.
Galadriel is supposed to be banned from return because she associate with the kin-slaying in Alqualondë or at least continued on from Aman and then was banned from return.
After the War of Wrath, with the downfall of Morgoth and the destruction of Thangorodrim, Sauron adopted a fair form and repented his evil deeds in fear of the wrath of the Valar.
