Naruto could inherit Alucard's ability to control familiars. In the Naruto universe, he could use this to control shadow clones in a more powerful and efficient way. Instead of just creating basic clones, he could endow them with some of Alucard's vampiric traits. Additionally, he might gain the power of Alucard's hypnotic gaze. With this, he could potentially paralyze his opponents or make them see illusions during battle.
He would likely gain Alucard's regenerative abilities. So if Naruto got injured in battle, he could heal extremely quickly, much faster than his normal Uzumaki healing factor. Also, he might be able to turn into mist or some other intangible form like Alucard can, which would give him an edge in combat, allowing him to avoid attacks and surprise his enemies.
Naruto would gain super strength. He could lift extremely heavy objects with ease, like mountains or large buildings in the Naruto world. He would also have super speed, enabling him to move faster than any ninja technique. And of course, he would be able to fly, which is a completely new ability in the Naruto universe.
He might gain enhanced senses like better hearing and smell, which are common for hanyous. This would help him in tracking enemies or sensing danger even before it's visible. Also, he could have increased physical strength and speed. His already impressive ninja skills combined with the hanyou powers could make him a formidable fighter in close combat.
He might have the ability to regenerate like Alucard. Naruto is already known for his large chakra reserve, but if he were like Alucard, his body could heal from almost any wound instantaneously. Also, he could potentially have some form of blood - based power, like Alucard's control over his blood. Maybe he could use his blood to create weapons or clones in a more macabre way compared to his normal shadow clones.
One of the new abilities Naruto would gain is enhanced stealth. Shadow the Hedgehog is known for being able to move quietly and blend into the shadows. Naruto, as Shadow, could use this ability to surprise his enemies. He could lurk in the shadows, waiting for the perfect moment to strike. Additionally, he might gain the power to levitate or glide short distances. This would add another dimension to his movement in battle, allowing him to quickly change his position in the air and attack from unexpected angles. His sensory abilities might also be enhanced, being able to detect the presence of enemies from a greater distance, much like how Shadow can sense threats in his own world.
Well, if Naruto becomes a Sannin, he would surely gain some amazing new abilities. For one, he could inherit Tsunade's healing abilities. This would be a great addition to his skills as he could not only fight but also heal his comrades on the battlefield. In terms of Jiraiya, Naruto might be able to master more advanced forms of Rasengan, inspired by Jiraiya's own jutsu creativity. And from Orochimaru, he could get a better understanding of the chakra nature and how to manipulate it in more complex ways, like Orochimaru did with his snake - like jutsus.
Naruto could develop the ability to better understand and manipulate the chakra of others. His maturity might give him the wisdom to see the flow of chakra in different ways. Additionally, he may gain the ability to quickly analyze battle situations and come up with more creative solutions due to his increased mental maturity.
One possibility is that he gains enhanced speed and stealth. As a chunin, he'd need to be more covert in his missions. He could learn to move so quietly that even sensors would have a hard time detecting him. And his speed could be on a level where he can quickly close the gap between him and his enemies without them realizing it until it's too late.
He would definitely gain Deadshot's incredible marksmanship skills. Naruto, who was already good at aiming his Rasengan and other attacks, would now be able to use firearms with extreme precision. His new ability might also include Deadshot's stealth skills. Naruto, who was used to sneaking around in his ninja world, would now be able to blend into the shadows even better in a more urban and modern setting like Deadshot's world.
If we consider their abilities, Naruto has his various jutsu like the Rasengan and Shadow Clone Jutsu. Female Alucard, assuming she has similar powers to the original Alucard, has superhuman strength, speed, and the ability to transform. In a fanfiction, they could combine their powers in combat. For instance, Naruto could use his Shadow Clones to distract an enemy while Alucard sneaks up and uses her strength to deliver a powerful blow.
He could gain the ability to use a katana with great skill. Since samurai are known for their swordsmanship, Naruto would likely train hard to master it. He might also develop new chakra - based attacks that are more in line with samurai techniques. For example, he could create a chakra - enhanced slash that has the power of a samurai's strike.