Well, Naruto as a demon god could possess the ability to control the elements in a more extreme way. For instance, his fire jutsu could be so powerful that it could incinerate entire forests in an instant. His water jutsu might be able to create massive tsunamis with just a thought. He could also have some sort of mind - control or influence ability, which he would have to be careful not to misuse. And his healing factor could be off the charts, making him almost invincible in battle.
If Naruto were born as a Demon Fox Lord, he would likely have enhanced physical abilities. His speed, strength, and agility would be far greater than in the original story. He would also have better control over chakra, especially the chakra related to the Nine - Tails. He could probably transform into a more powerful fox - like form more easily and for longer periods. His senses would be heightened, being able to detect enemies from a greater distance and sense their intentions better.
If Naruto became an Arrancar, he would likely gain the ability to use Cero. Cero is a powerful energy blast that Arrancars can fire from their mouths or hands. He might also be able to use Sonido, which is a high - speed movement technique similar to the ninja's Shunshin no Jutsu. His physical strength and durability would probably increase significantly as well.
He might also have enhanced physical abilities. Basilisks are large and strong snakes. So Harry in basilisk form could be extremely fast, with great strength to coil around and constrict his enemies. And he would likely be able to move very quietly, making it easier to surprise opponents. Also, being a basilisk might give him a connection to other snake - like creatures. He could communicate with them, or even control them to some extent, which could be useful in a fight or for gathering information in the wizarding world.
He would likely have enhanced versions of his existing abilities. His speed, which was already remarkable as a ninja, would be god - like. He could move so fast that he would seem to be in multiple places at once, much like the gods' ability to teleport or move at incredible speeds. His strength would also be magnified, allowing him to lift mountains or large structures with ease.
Naruto's chakra - based abilities would probably be combined with Deathstroke's combat skills. For example, he could use his Rasengan while also making quick, precise slashes with swords like Deathstroke. His ability to sense chakra could be enhanced in a way that mimics Deathstroke's heightened senses in combat.
His physical abilities would likely be enhanced. Red Lanterns have increased strength, speed, and durability. Naruto already has great physical prowess as a ninja, but as a Red Lantern, he could become even stronger. His ninjutsu might also change. For instance, his rasengan could be infused with red energy, making it more powerful.
His relationship with Sasuke would likely be very different. Sasuke might be more in awe of Naruto, but also feel a greater sense of distance. They would no longer be just rivals, but there could be a new power dynamic where Naruto is in a much higher position.
His relationships would change a great deal. With Sasuke, there might be a new level of respect. Sasuke would see Naruto in a whole new light, not just as a rival but as someone truly powerful. His friends like Sakura and Kakashi would be more in awe of him. They might feel a bit of distance at first, but Naruto would try to bridge that gap. His enemies would be either terrified or would try to use his new status to their advantage.
He would definitely have the Sharingan. With the Sharingan, he could copy jutsu more easily and have enhanced perception in battle. Also, he might inherit some of the Uchiha's fire - style jutsu, which would add to his combat abilities.
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.