"...and her hair was held a marvel unmatched. It was golden like the hair of her father and of her foremother Indis, but richer and more radiant, for its gold was touched by some memory of the starlike silver of her mother, and the Eldar said that the light of the Two Trees had been snared in her tresses."
Galadriel denied her hair to Fëanor because she knew the greed in his heart would never change. By gifting Gimli three hairs instead of the one he asked for, he proved a point that spanned back to the First Age.
Why did Galadriel give Gimli her hair but not Fëanor?
Fëanor was one who wished to possess and Galadriel had perceived this darkness within his heart. Gimli, on the other hand, wishes only to love in pure devotion and so she gives him not only one strand but three, recalling the three times that Fëanor had made his request and the three times that she had refused him.
For example, the Elven cloaks are not only protection, they symbolize the bonds of friendship between all of the members of the Fellowship of the Ring. Frodo's phial not only helps him escape from dark places but it symbolizes hope, both for Frodo and fans.
By this one act of daring, Gimli proves that he is not only respectable but self-effacing: he does not ask a gift for himself, but for the betterment of the relationship between the Mountain and the Wood. Galadriel granting his gift shows that she has compassion for the Dwarf due to knowing his heart.
Why did Galadriel Give Gimli Three Hairs? (Updated) Middle-earth Explained
Why didn't Boromir get a gift from Galadriel?
It may be related to their intention to play up the discord between Boromir and the rest of the Fellowship and the mistrust Galadriel felt toward him specifically. That angle was heavily emphasized throughout the film.
Feanor was so inspired by Galadriel's grace and beauty, that he wished to use strands of her hair in the making of his three Silmarils, the most precious gems ever created in Middle Earth.
Arwen. Galadriel's granddaughter and the daughter of Celebrían and Elrond. After the War of the Ring, Arwen marries Aragorn II Elessar and becomes Queen of the Reunited Kingdom of Arnor and Gondor. Like other Half-Elves, Arwen has the birthright to choose either immortality among the Elves or mortality among Men.
A Galadhrim bow strung with elf hair and arrows for Legolas. A small grey wooden box with a silver rune "G for Galadriel". Inside the box was earth from Galadriel's orchard. The box also contained a silver nut from a Mallorn tree, the last east of the sea and west of the mountains.
Although this relationship may have happened with Galadriel's meeting or not, it's clear Gimli's love for her expedited his ease in befriending Legolas.
Thus, Galadriel's dark form in Jackson's The Lord of the Rings personified what would have occurred had the Lady of Lothlorien given in to temptation and taken the One Ring for herself. She would have succumbed to evil because the Ring was indomitable, even with her power.
She had acquired power through Nenya which was also designed specifically for her. She probably learned a lot of lore from Melian and it claims the two spent time together in the Silmarillion.
Galadriel was one of the Ñoldor who came to Middle-earth wishing to see the lands and rule a realm of her own. She came with the second host of Elves from Aman with Fingolfin and Finrod. In Doriath, she and Celeborn fell in love and married.
After a time, Galadriel and Celebrían passed through Khazad-dûm and dwelt in Rivendell. There, she met Elrond, who, though he loved her, said nothing about it. In TA 109, Elrond wedded Celebrían. She bore him twin sons, Elladan and Elrohir in TA 130, and then a daughter, Arwen in TA 241.
For she also had an outstanding gift to see into the minds of others, and, though she judged most with kindness, she hated and feared the darkness in Fëanor, not perceiving that the shadow of the same evil had fallen upon the minds of all the Noldor, including her own.
Yet, since Tolkien does give family trees for other important Elves in the book, such as Galadriel and Elrond, it's clear that Galadriel is not Legolas's mother. (Besides, she is one of the Noldor, not a Silvan or Sindar Elf.)
In terms of genealogy, Elros would be Aragorn's great grandfather with about 60 "greats." This makes Elrond Aragorn's great, great, etc. uncle, and since Arwen is the Lord of Rivendell's daughter, she and Aragorn are first cousins many times removed.
As previously stated, Gandalf is a Maia and is therefore superior to Elves regarding power. Still, this isn't to say that an elf couldn't develop enough skill and power to defeat a Maia. As a bearer of one of the Three Elven Rings (Nenya), Galadriel would have an edge against Maiar like Saruman and Radagast.
Before the Company of the Ring left Lothlórien, each of its members was presented with a gift by Galadriel. Boromir was given a belt of gold which he carried in the journey until the Breaking of the Fellowship. When Aragorn, Gimli and Legolas laid him in his burial boat, the golden belt gleamed about his waist.
A legend says that the Wizard Gandalf had brought such a stone, called the Elessar, from Valinor. He gave the Elessar to the Elven Lady Galadriel and remarked prophetically that she would pass it to another, who will also be called Elessar. From this would come Aragorn's royal name Elessar (Quenya for "Elfstone").
Upon thinking, Finrod whispers to her: "Sometimes we cannot know until we have touched the darkness". To this, Galadriel ponders that it sounds simple and Finrod tells her that many things are, but she must decide them for herself as he will not always be there to help.
According to one theory (via Stack Exchange), Gimli did not know about the fall of Moria in The Lord of the Rings: The Fellowship of the Ring movie due, effectively, to poor communication.
It is also stated in Unfinished Tales that Gimli was prevented from traveling with his father on the Quest of Erebor because Thorin and Company thought him too young, though Gimli, being in his sixties, considered himself ripe for adventure and was disappointed to be left behind.
