One main theme is often power. Exploring the potential power of Rin's Sharingan, how it compares to other Sharingan in the Naruto world. Another theme can be sacrifice. Given Rin's fate in the original series, fanfictions may explore the sacrifices related to her Sharingan, like she might have sacrificed her own well - being to protect others with its power.
One popular 'naruto rin sharingan fanfiction' is 'The Rin's Legacy'. It delves into how Rin's Sharingan could have had a greater impact on the Naruto universe if she had survived. Another is 'Sharingan of Rin: A New Path' which creates an alternate storyline where Rin's Sharingan powers are explored in a different way, with her having unique abilities that change the course of many events in the ninja world.
In fanfiction, Naruto could get the Sharingan through a blood - related connection that is revealed later. For example, it could be discovered that he has some distant Uchiha ancestry that gets activated somehow. Maybe a powerful enemy's attack awakens this dormant Uchiha blood in him, and as a result, he develops the Sharingan. It could also be that a powerful sage or a new character uses their own unique powers to bestow the Sharingan upon Naruto for a specific purpose.
If Naruto had the Sharingan in fanfiction, it would likely lead to some interesting power - up scenarios. He could combine the power of the Sharingan with his own massive chakra reserves. This might make him an even more formidable opponent. His training would also take a new turn as he'd have to learn to control and master the Sharingan's abilities, like the different levels of the Sharingan and their unique powers.
Naruto might adapt by first trying to understand the basic functions of the Sharingan. He could start with the simple ability to see chakra flow more clearly. Since he has always been perceptive about people's emotions, he could use the Sharingan to read the emotions of his enemies through their chakra, which would help him in battles.
In a fanfiction world where Naruto and Rin have a baby, it could be a very interesting story. Maybe the baby would inherit Naruto's positive attitude and Rin's kindness. The story could explore how they raise the child in a world full of challenges and ninjas.
One drawback could be the strain on his body. The Sharingan is a powerful dojutsu, and Naruto's body, which is used to his own chakra system, might not be able to handle it well at first. This could lead to fatigue and over - exertion during battles.
In this fanfiction concept, Naruto and Sasuke as brothers could lead to a very different Naruto universe. With Sasuke having the Sharingan, he could potentially use it to protect Naruto more often. Maybe they would train together in new ways, combining Sasuke's Sharingan - related jutsu with Naruto's Uzumaki power. For example, Sasuke could use his Sharingan to analyze Naruto's chakra flow and help him master new forms of the Rasengan faster.
Yes, in some fanfictions, Naruto is given the Sharingan. Fanfiction writers often like to play with the concepts and powers in the Naruto universe, and giving Naruto the Sharingan can lead to some really interesting storylines. It might be a result of some kind of power transfer or a unique plot device.
One possible fanfiction could be that Naruto is on a mission and encounters a powerful Uchiha who, instead of killing him, transfers his Sharingan to Naruto for some mysterious reason. Naruto then has to learn to control this new power while still maintaining his own unique ninja style.