He could be touched. Despite his stoic exterior, Itachi may see this as a genuine and innocent gesture from Naruto, and it could warm his heart in some way. Maybe he starts to see Naruto in a new light, as someone who can bring a bit of light - heartedness into his world of shadows.
Naruto might give Itachi some traditional Konoha food as a gift. Since Itachi has been away from the village for a long time, he might miss the taste of home.
A simple plot could be that Itachi entrusts Naruto with his Sharingan because he believes Naruto can use it to bring peace to the ninja world. Naruto, being the kind - hearted person he is, accepts the responsibility. He starts training with Kakashi to understand and master the Sharingan's powers. With the Sharingan, Naruto can anticipate his opponents' moves better and uses this advantage in battles against powerful enemies like Pain.
I'm not sure about a specific one off - hand, but you can check out fanfiction websites like Fanfiction.net or Archive of Our Own. Just search for 'Itachi gives Naruto power' and you'll likely find a bunch of different stories. Some might focus more on the action aspect, while others might explore the emotional side of Itachi's decision to give Naruto power.
This would be a huge change for Naruto. Firstly, the Sharingan's ability to see chakra flow would let Naruto analyze his opponents' weaknesses more accurately. He could potentially use this to improve his Rasengan or develop new jutsus. Moreover, in terms of combat, he could enter genjutsu battles on a more equal footing, which was something he previously struggled with due to his lack of natural genjutsu skills.
One possible plot implication is that it could create a rift between Naruto and some of the shinobi in the village. Since the Sharingan is an Uchiha - specific power, some might be suspicious of Naruto having it. Another is that it could lead to Naruto being targeted by those who want the Sharingan for themselves.
Well, Naruto already has his own powerful abilities like the Nine - Tails' chakra. But with Shisui's Sharingan, his perception skills would be enhanced. He could probably anticipate attacks better and maybe even use some basic Sharingan - related genjutsu. However, it would also be a challenge for him to master as he has no prior experience with the Uchiha's dojutsu.
Well, the plot could start with Itachi realizing that Naruto is the key to the future of Konoha and the ninja world. So, he gives Naruto his Sharingan. Naruto then has to deal with the new power. He might start having visions related to Itachi's past, which could help him understand the Uchiha - Senju conflict better. And this new knowledge could influence his decisions in future battles and political situations in the ninja world.
One interesting aspect of Naruto Rule 63 Itachi fanfiction could be exploring Itachi's character from a different gender perspective. In these fanfictions, Itachi might have different relationships with other characters. For example, his bond with Sasuke could be portrayed in a new light, perhaps with more emotional nuances due to the gender - swap. Also, the way he approaches his mission and his loyalty to the village could be re - examined through this new lens.