Perhaps he could have some sort of dark - based chakra manipulation. Demons usually have unique chakra, and Naruto's demon part might allow him to use a different form of chakra that gives him new jutsu, like the ability to create shadowy clones or dark - energy attacks.
Well, Naruto could have a range of reactions. On one hand, he might feel a sense of isolation, thinking that he's different from all the other ninjas he knows. But on the other hand, his adventurous spirit could also make him curious about what this new part of him means. He might start to wonder about his powers and how they relate to his demon heritage. He could also be a bit scared, especially if he has been taught to fear demons in the ninja world.
He might gain enhanced physical strength. The devil gene could give him a boost in his taijutsu skills, allowing him to overpower opponents more easily.
She could gain powers related to female energy in magic. Maybe she could master spells for healing or protection on a much larger scale. For example, she could create a powerful shield around a whole village.
He might have powers like shape - shifting into a more demonic form. Maybe he could have the ability to breathe fire or some other elemental powers related to chaos or destruction. He could also have enhanced strength and speed that are far beyond what a normal ninja has, and his senses could be super - sharp to detect danger or prey.
He could gain the power of controlling water like Poseidon's kids since he has good chakra control. It would be a new addition to his skill set.
He could gain super strength, allowing him to overpower enemies more easily than before. His speed would be enhanced to a level that might make him almost impossible to catch. And he could have the power of hypnosis, which would be useful in combat and getting information from foes.
He could probably gain the ability to phase through objects. Just like wraiths are often depicted as being able to pass through solid things. This would give him an edge in combat and also in sneaking around.
Well, for one, she could inherit the vampires' immortality which in itself is a huge power. In addition to that, given the Cullens' unique abilities, Hermione might gain something related to her senses. Maybe her vision could become extremely sharp like a vampire's, allowing her to see in the dark or detect the slightest movements. And considering her magical background, there could be an interesting fusion of her magic with the vampire powers. For example, she could use her magic to enhance her new vampire - like abilities even further, creating a whole new set of powers that are unique to her within the Cullen family.
One possible power is the ability to produce honey. This might seem strange, but in a fanfiction world, it could be used in various ways. For example, he could use the honey to heal wounds, as honey has some natural antibacterial properties. Another power could be related to the bees' communication. If Naruto can understand the bees' complex communication system, he could use it to send coded messages or even disrupt the communication of his enemies if they also use some form of insect - based communication.
He might have enhanced physical strength due to his demonic nature. For example, he could be able to lift heavier objects or run faster than normal. Also, he could have some sort of dark - based jutsu, like summoning shadowy creatures.