A prevalent theme is transformation. The dragon might cause Naruto to undergo some kind of transformation, either physically or in terms of his abilities. Additionally, there are themes of mystery. The origin of the real dragon and its purpose in the Naruto world can be a big mystery that Naruto has to solve. And of course, there's the theme of heroism. Naruto, with the help of the dragon, might have to save his world from some new and greater threat.
Yes, there are some. You can check out fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Naruto has real dragon' and you'll find a variety of stories. Some might be about Naruto encountering a real dragon in his world, or perhaps having some kind of special connection with one.
In some fanfictions, Naruto might obtain the dragon sword through a special quest. Maybe he stumbles upon an ancient temple during one of his missions where the sword is hidden as a powerful artifact, guarded by some kind of magic or traps. He overcomes these obstacles using his ninja skills and determination, and thus gets the dragon sword.
Well, one implication could be enhanced physical abilities. Dragons are often seen as strong and powerful creatures in many mythologies. So Naruto might have greater strength, speed, and endurance. He could also have some sort of elemental control related to dragons, like breathing fire or manipulating wind in a more dragon - like way. Maybe he could even fly in some forms, as dragons are known for their flight ability.
One common theme is power - the dragon gives Naruto an extra boost of power which he uses to face stronger enemies. For example, in many stories, the dragon's strength is combined with Naruto's own to defeat Akatsuki members.
In fanfiction, the concept of seeing the'real' Naruto can be quite subjective. Kakashi, being a perceptive character, could potentially see the real Naruto in different ways. It could be when Naruto shows his vulnerability regarding his past, like his loneliness as a child. Or it could be in a situation where Naruto's true ninja skills, not just his brute strength, are on display and Kakashi witnesses this new side of him.
Maybe the dragon sword has the ability to absorb chakra. When Naruto is in a fight, he could use this to his advantage by draining his opponents' chakra through the sword when it makes contact. This would weaken his enemies and at the same time, the absorbed chakra could be used to power up the sword's other abilities.
Maybe it would be an ice - dragon. This would be an interesting contrast to Naruto's usual warm - natured self. The ice - dragon could have blue - white scales and the ability to freeze things with its breath. It could also create ice - bridges or walls in battles, providing a unique strategic advantage for Naruto.
The scales might give him new jutsu capabilities. For instance, he could learn to use the scales to create a sort of dragon - scale armor jutsu, where he can cover himself in a protective layer of scales that also has offensive capabilities, like shooting out sharp scale - like projectiles.
There's also a fanfiction where Naruto is gifted a dragon by a mysterious sage. The dragon has unique abilities like breathing different elements which Naruto has to learn to control. It adds an interesting twist to the Naruto storyline as he has to train with the dragon and integrate its powers into his own fighting style.