Natsu's usually carefree and fun - loving personality could take a darker turn. Trained by Acnologia, he might be exposed to a more cutthroat world view. He could become more calculating in his battles, rather than relying on his usual instinctive fighting style. His sense of humor might also fade a bit as he becomes more focused on his newfound power and the responsibilities that come with it. He might even start to question the values of Fairy Tail, like their emphasis on friendship, if he starts to believe that power is the only thing that matters in the world of magic.
His confidence might become more of an overbearing arrogance. Since Acnologia is so powerful, Natsu could start to think he's invincible after being trained by him. He might become more solitary too, as Acnologia is often depicted as a lone figure. Natsu might start to distance himself from his Fairy Tail friends because he feels he's on a different level now.
Natsu's personality could change in several ways. He could become more ruthless. Acnologia is not known for his mercy, and some of that might rub off on Natsu. He may be quicker to anger and less likely to hold back in a fight. However, his core of loyalty might still remain, but it could be tested. For example, if Fairy Tail was in danger because of his new, more dangerous powers, he would have to figure out how to use his strength without causing harm to his friends.
Naruto might become more sly. Since Loki is a trickster, Naruto could pick up some of his devious ways. He may not be as straightforward as he used to be.
His personality might become more brooding. With Darth Vader's influence, Naruto could lose some of his naivete and become more cautious.
His personality might change in several ways. He would probably be more humble as he realizes the vastness of the power he is being exposed to. Also, he could become more of a mentor - like figure to the younger ninjas in Konoha. Since he is getting trained by such a powerful entity, he would have a greater sense of responsibility and would want to pass on his knowledge. He might also become more open - minded, as the Grand Priest's teachings could expose him to new ways of thinking and different cultures if the fanfiction has elements of different universes interacting.
If Harry Potter was raised by Natsu, his personality would change drastically. Natsu is a very passionate and hot - tempered character. Harry would be influenced by this passion and would be more driven in his pursuits. He would no longer be the meek boy who was bullied by the Dursleys at the start. Instead, he would be more confident and assertive. His sense of justice would also be more like Natsu's, which is more about immediate action rather than following a set of bureaucratic procedures. He would probably have a stronger sense of loyalty towards his friends as well, because Natsu values friendship above all else and would instill this value in Harry.
He might become more cautious. Tsunade is a more calculating ninja compared to some of Naruto's previous mentors. So Naruto could start to think before he leaps, rather than just charging into battle head - first all the time.
His confidence could take on a different form. While Naruto has always been confident in his abilities, training with Zoro would make him more self - assured in a more reserved way. Zoro's tough training would force Naruto to prove himself not just to others but also to himself, and this could lead to a more mature kind of confidence. Also, Naruto might become more introverted as he focuses more on his training, similar to how Zoro is often focused on his own improvement.
If Natsu were trained by Acnologia, he might face a moral dilemma. Acnologia is a feared and often seen as an evil force. Natsu has always been on the side of good. So, during the training, he would have to decide whether to follow some of Acnologia's more ruthless ways of using power or stay true to his own values. This internal struggle could add a lot of depth to his character. Also, his relationships with his friends in Fairy Tail might be strained as they might be worried about the influence Acnologia has on him.
Harry's personality could become more disciplined. Beerus is all about discipline in his training. So, Harry would have to follow strict rules. This could make him more focused and less impulsive in his actions, which is a big change from his sometimes reckless nature at Hogwarts.
His confidence might increase even more. Female Madara is a strong figure, and being trained by her would give Naruto a sense of having access to greater power. So he would be more self - assured in his actions.
His personality could become darker. Darth Vader's influence might make Naruto more brooding and less of the optimistic character he is. He could start to value power more than friendship at times.