Usually, only Elves and higher beings would be allowed to travel into the West, but with Gimli being as stubborn as ever, he decided to tag along with Legolas not only because he wanted to stick by his friend but because he also wished to lay eyes on the beauty of Galadriel one more time.
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.
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.
By special permission of the Valar, the Hobbits Frodo Baggins, Bilbo Baggins, and Samwise Gamgee were also permitted to go to Valinor, as they had once borne the One Ring of Sauron. Later, after the death of Aragorn, Legolas the Elf would sail to Valinor and bring with him Gimli the Dwarf.
After Aragorn's death, Legolas made a ship in Ithilien and left Middle-earth to go over the sea. His strong friendship with Gimli prompted Legolas to invite him to accompany him to the Undying Lands; making him the first and only Dwarf to do so. He was never seen again in Middle-earth.
Why Couldn't Men Live in the Undying Lands? | Lord of the Rings Lore | Middle-Earth
What happens to Legolas after Gimli dies?
Eventually, Legolas came to Ithilien with some of his people, with his father's leave, to live out his remaining time in Middle-earth helping to restore the devastatedforests of that war-ravaged land.
It is later mentioned that Tauriel is a talented warrior and was therefore made leader of the Mirkwood border guards. Legolas, the son of Mirkwood's Elven king Thranduil, is indicated to be attracted to her, but as she is a lowly Silvan Elf, she does not believe herself worthy of him.
Being one of the chief leaders of the Noldorin rebellion, Galadriel was not allowed to return and a ban was set upon her, to which she replied that she had no wish to do so.
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.
This is implied in the Akallabeth, where men might be 'burnt out' by too much proximity to the Ainur. However, the refusal of the Valar to admit men may also be a consequence of men being corrupted early after awakening by Melkor, or his agents.
Gimli is not the last of the dwarves. This is a common misconception because Gimli is the only dwarf who gets a fair amount of coverage in the franchise. Lord of the Rings focuses its narrative primarily on the affairs of men, elves, and hobbits. Dwarves are a secluded race that lives in the mountains.
Gimli was 139 years old (born in 2879 of the Third Age) when the Fellowship of the Ring set out from Rivendell, making him 52 years older than Aragorn.
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. Men are mortal, and when they die they go beyond the circles of the world, even the Elves not knowing where that might be.
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.
Only Elves and those deemed worthy (like Gandalf and Frodo) could sail to the Undying Lands. And by choosing to stay with Aragorn, she was forgoing her place on the boats and binding herself to the realm of men, thus becoming mortal.
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.
Gimli didn't know about Moria's fate because there had been no communication between Erebor and Moria for 25 years, and the Dwarves were hopeful and did not want to accept failure until there was certain news.
As in the latter case, the Elves were too busy defending their own homes from Sauron's (and Saruman's) growing power and couldn't spare their dwindling fighters to help the Men. Elrond's sons, Elladan and Elrohir, also defended Gondor during the Battle of Pelennor Fields.
Assuming the One Ring was destroyed, Galadriel's ring would also start to fade, causing Lothlórien to lose its glory and magic. So, when Galadriel refused the One Ring, she wasn't just sacrificing her desire to rule. She knew that she was sacrificing her kingdom and its well-being for the sake of peace in Middle-earth.
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.
Put simply, the Elves can't return to Valinor in The Rings of Power because their work in Middle-earth is unfinished. There is far more context to the situation in Tolkien's writing, but The Rings of Power skipped The Silmarillion's complexities regarding Elves and the War of Wrath.
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.
Tauriel gave her love to Kili in the movies. In “Laws and Customs of the Eldar”, or LACE, it talks about elves, and that they do not marry unless they truly love one another.
