Bilbo kept the Ring a secret primarily because it gave him a sense of power, invisibility, and escape, but also because he was slightly ashamed of how he'd acquired it (winning it from Gollum) and didn't fully understand its evil, while Gandalf initially allowed it due to his trust in Bilbo, the Ring's seemingly harmless nature in Hobbit hands, and the wisdom of keeping such a dangerous item hidden and un-used.
Gandalf allowed Bilbo to keep the Ring initially because he did not realize it was the One Ring and believed it to be a harmless magical item. His trust in Bilbo and the absence of any immediate threat led him to see no reason for concern.
Frodo sails to the Undying Lands because the Ring's wounds--physical, psychological, and spiritual--left him unable to find full healing in Middle-earth. The voyage is a merciful, honored cure offered by the Valar and Elves, fitting both the character's sacrifices and the mythic structure of Tolkien's world.
One of the effects of the ring is that it takes you to the unseen world. That is why Frodo and Bilbo become invisible. Sauron exists in both worlds. Therefor the ring doesn't move him anywhere and he remains visible.
It's possible that Gollum's prolonged search for the ring allowed it to maintain a significant power over him, suspending his aging process. In contrast, Bilbo's exposure to the ring's influence waned after he willingly (mostly) relinquished it, allowing his aging to resume more noticeably.
It's not the years; it's the mileage. Gandalf isn't a Maia in the same way Sauron is. He was sent to middle earth as an old man, so his body is much more real than Sauron's “raiment”. He can't use his power to the same extent, he can't change his forms at will.
Tolkien's description of Gollum conforms to a Catholic – and Thomistic – account of envy, which is a “sadness of the soul”; and it is Gollum's unbearable sadness and his unquenchable desire for the one Ring that marks his character.
Gandalf does not WANT to touch the ring. Just as Galadriel resists the temptation to take it when Frodo offers it to her willingly. And all this because "Power Corrupts". Sauron and the Ring are allegories for the corruption that inevitably arises when too much power is concentrated in one place.
Why was Sauron afraid of Aragorn potentially possessing the Ring? Gandalf explains it in the Return of the King (during the council after the battle of the Pelennor fields) that Sauron would never think somebody would want to destroy the One Ring.
The name "the Undying Lands" does not mean that the land itself causes mortals to live forever. Generally, only immortal beings are allowed to reside there.
Tolkien's Legolas is extremely introverted. He just doesn't have much to say directly to anyone, perhaps because he's thousands of years old. His odd relationship with Gimli draws him out in a way the hobbits never do, and that's mostly after Frodo and Sam leave the Fellowship.
Midway through The Lord of the Rings, Gandalf becomes the head of the order of Wizards, and is renamed Gandalf the White. This change in status (and clothing) introduces another name for the wizard: the White Rider. However, characters who speak Elvish still refer to him as Mithrandir.
But that's actually the answer: Eru Said So . The Undying Lands are a place for immortal beings (Eldar), and mortals are forbidden from entering.
Bilbo evades him and hides behind a massive pillar, still under the cloak of the ring. Smaug continues his search and claims that he is aware of the Ring in Bilbo's possession and that he sensed that Bilbo has something "made of gold, but far more precious," which in turn forces the Hobbit to remove the Ring.
Power was never going to succeed in defeating evil. Gandalf was at exactly 12.35% of his full power as Gandalf the Grey, this went up of 18.237% as Gandalf the White. The Maia varied greatly, as did the Valar. Even at his fullest, Olorin/Gandalf was not the equal of Mairon/Sauron, not even close.
Instead, we have to consider that Sauron, the original owner, is not human, but has a quasi-divine status. Therefore ownership of the Ring is subject to Divine Law. With this precedent in mind, many of the ambiguities clear up nicely. After numerous transfers by violence and trickery, Frodo is the true owner.
As one of the Maiar, Gandalf was not a mortal Man but an angelic being who had taken human form... along with the other Maiar who entered into the world as the five Wizards, he took on the specific form of an aged old man as a sign of his humility...
Elrond chose the fate of the Elves and therefore the choice was presented to his children. The reason why Eldarion and his sisters (the children of Aragorn and Arwen) were born mortal was because Arwen chose mortality and therefore that fate was passed on to the rest of their line.
Sauron needed Gandalf out of the picture permanently, as he was the only enemy with the knowledge, leadership and determination to thwart him. His biggest mistake was ego. He succeeded by trickery, by his ability to deceive others. He conquered so much land that his ability to control became out of reach .
Aragorn would have followed Frodo to the end, and he could have tried to catch up with Frodo, but this would basically go against the wishes of the ring bearer, abandon his friends, and lead to revealing the Council of Elrond's plans to destroy the ring and sneak into Mordor.
While Bilbo's ring certainly concerned him, it took years for Gandalf's suspicion (and lack of success in finding Gollum to interrogate) to lead to him to search the archives of Minas Tirith for any identifying information on the One Ring. The inscription revealed by fire was only known to Isildur.
He's generally forbidden to use his powers to directly influence events in Middle Earth. He's supposed to be more of an advisor/cheerleader-type figure who helps the people of Middle Earth work to solve their own problems rather than them relying on divine intervention.
The clearest same-sex relationship in the novel, in the eyes of scholars, is that of the ringbearer Frodo Baggins and his servant, originally his gardener, Sam. Tolkien described their relationship as like that of an officer in the British Army and his military servant or batman.
Merry and Pippin both died decades BEFORE Aragorn died. Merry and Pippin died in FA 63, while Aragorn died in FA 120 - and it was after this that Legolas and Gimli sailed to the Undying Lands. All of this is made patently clear in Tolkien's own timelines.
Melkor is the most powerful of the Valar but he turns to darkness and is renamed Morgoth, the primary antagonist of Arda. All evil in the world of Middle-earth ultimately stems from him. One of the Maiar of Aulë betrays his kind and becomes Morgoth's principal lieutenant and successor, Sauron.