His physical abilities would be enhanced. Constantly running, climbing, and fighting in the forest would make him stronger and more agile. His stealth skills would be top - notch as he'd have to hide from the forest's predators.
Naruto could have a greater control over his chakra. Since Kushina would be there to guide him, he would likely avoid some of the pitfalls he faced in the original story. His physical strength might also be enhanced as Kushina could train him in ways that utilize his Uzumaki bloodline more effectively.
In a fanfic where Naruto is raised in the Forest of Death, he might become extremely tough. He'd have to fight for survival from a young age. Maybe he'd befriend some of the dangerous animals there, learning their ways to stay alive. He could also develop unique ninja skills by adapting to the harsh environment of the forest.
In this fanfiction, Naruto could be isolated in the Forest of Death. He has to fend for himself, which means he has to figure out how to get food, water, and shelter all on his own. This experience might make him more self - reliant and independent. He may also develop a different view on the concept of family and friendship since he has been alone for so long.
His chakra control would probably be better. In a temple, he might learn meditation techniques that help him master his chakra more effectively. Also, his physical abilities could be more refined in terms of balance and grace, like a monk's movements.
Naruto's combat style would be more refined. Sakumo was a highly skilled ninja, and he would teach Naruto better swordsmanship skills perhaps. Naruto's taijutsu could also be more precise and calculated. Also, Naruto might develop better chakra control earlier, as Sakumo could instill in him the importance of efficient chakra usage from a young age.
Naruto would be more in tune with nature. He would understand the rhythms of the forest, the behavior of animals, and the flow of natural energy better. This could potentially lead to him having an easier time mastering Sage Mode, if that is part of the fanfiction's storyline. His view of the world would be narrower in some ways, as he has only known the Forest of Death, but broader in others, as he has a deep understanding of the natural world that most ninjas lack.
Yes, there are likely some fanfics out there with such a plot. Fanfic writers often explore alternate storylines, and this would be a very dark and dramatic deviation from the original Naruto story.
A fanfic combining Naruto's Forest of Death and Devil May Cry could be really interesting. It might involve characters from Naruto having to face the demons and challenges similar to those in Devil May Cry. For example, Naruto and his team could enter a strange realm in the Forest of Death that has elements of the Devil May Cry world, like encountering powerful devil - like creatures. They would then have to use their ninja skills along with some new abilities inspired by Devil May Cry to survive and complete their mission.
Naruto's ability to control the Nine - Tails would be enhanced. Since the Sage has a deep understanding of the tailed beasts, he could teach Naruto how to fully harness the power of the Nine - Tails without the usual struggle. This would make Naruto not only stronger but also more in tune with the beast's power, allowing him to use it more effectively in combat. He could also potentially communicate with the Nine - Tails on a much deeper level, leading to new forms of cooperation between them.
His abilities might take on a more unpredictable edge. He could incorporate some of Joker's trickery into his combat. For example, using misdirection like Joker does in his schemes.