He'd adapt by being his usual curious self. Naruto is always eager to learn new things. So, he'd start by observing the classes and how things work at the academy.
In a fanfiction, Naruto's adaption to True Cross Academy would be a process. At first, he might be confused by the different rules and the whole concept of exorcism. But as time goes on, he'd start to pick up on things. His natural athleticism would help him in the physical training aspects. And his experience in facing powerful enemies in his own world would give him the confidence to face the demons in the academy's world. He might even try to combine his ninja techniques with what he learns about exorcism to create his own unique way of dealing with threats at the academy.
Naruto would likely be an outlier in the social hierarchy. He doesn't come from the vampire - hunter world, so he wouldn't fit neatly into the existing groups. However, his friendly and outgoing nature might make him popular among some students. He could start his own little group of friends who are interested in his ninja ways.
Naruto would adapt by using his ninja skills. His speed and agility from being a ninja would help him in exploring Earthland. He could also use his rasengan as a powerful attack against any potential enemies. He might start by finding a place to stay and learning about the local customs.
He'd probably start by observing. Naruto is curious, so he'd watch how the Asgardians live, their customs, and how they interact. Then he'd start to adapt by using his ninja adaptability skills.
Well, he might use his ninja skills to stand out. For example, his shadow clone jutsu could be a big surprise in the academy. Maybe he'd get into some friendly competitions with the students there, like in a physical training session.
Sasuke would likely be very cautious at first. He'd be observing everything closely, trying to figure out the rules of this strange place. His Sharingan might give him an advantage in seeing through some of the illusions in Wonderland. Naruto, on the other hand, would probably be more excited and jump right into things, ready to make friends with the odd - looking creatures.
To adapt to being the Mandarin, Naruto would first need to understand the nature of the ten rings. He might start by experimenting with each ring's individual power. He'd then figure out how to combine these powers with his existing ninja abilities like rasengan. His relationships with other characters would also change. Some might be afraid of his new power, while others would see it as an opportunity to fight against greater threats. Naruto would have to convince them that he can be trusted with this power and that he'll use it for the greater good.
He would likely start by observing. Just like how he was trained in the ANBU to be aware of his surroundings. He'd watch how the classes are conducted, how the students interact with each other and the teachers. Then he'd start to adapt by using his ninja skills in a way that fits the Hogwarts environment. For example, using his speed to get around the castle quickly.
Naruto would adapt slowly. At first, he'd be confused by the different lifestyle. But his adaptable nature would help. He might start by learning about the local customs and trying to fit in at school. He'd use his ninja skills in secret, like using his speed to be on time for classes when he oversleeps.
He would adapt in several ways. Firstly, Naruto's strong will would keep him going. He'd have to get used to the harsher living conditions and the different rules of war. He may have to tone down some of his more flamboyant moves at first to avoid attracting too much unwanted attention. He would also need to communicate effectively, which could be a challenge as the language and communication styles might be different. But as he gets to know the people, he'd start to blend in and use his skills to make a positive impact on the era.
In a 'Naruto travel to the future fanfiction', Naruto would adapt through his strong sense of curiosity. He would be eager to explore every new thing he sees in the future. His resilience would also play a big role. If he encounters difficulties, like not understanding how a particular future - tech works, he won't give up. Instead, he'll keep trying until he figures it out. And his ninja training gives him discipline. He would use this discipline to study the new ways of life in the future, from the social norms to the technological advancements.