Izuku's relationship with the villains would be completely transformed. Some villains might see him as a potential ally or a tool to be used. Others might fear him more than before. As for the heroes, there would be a split. Some would trust Izuku's good nature and believe he can use the All for One quirk for the betterment of society. But there would be others who would be very skeptical and might even try to stop him from using it, thinking it's too dangerous a power for anyone to possess, let alone Izuku who was once a quirkless boy.
With his classmates, some might be scared of Izuku. They've known him as a kind - hearted person, but the All for One quirk has such a dark reputation. However, some like Ochaco might try to understand him better and support him through his journey with this new quirk. His relationship with the teachers would also be under scrutiny. They would need to ensure that Izuku doesn't use the quirk for evil purposes, which could lead to a lot of extra monitoring and a sense of unease in their interactions.
His relationship with All Might would become extremely complicated. All Might, who passed on One For All, would be shocked and perhaps a bit disappointed that Izuku now has the All For One quirk. He might question his decision to choose Izuku as his successor. With Bakugo, their rivalry could take a different turn. Bakugo might be both envious and afraid of Izuku's new power, leading to more intense confrontations. And with his friends like Iida and Ochaco, they might be initially hesitant around Izuku, not knowing if he can still be trusted with such a villainous - associated quirk.
A fanfic with Izuku having a sand quirk could explore his new power dynamics. He would have to adapt his fighting style completely. Instead of using his original strength - based moves, he'd rely on the versatility of the sand. He could potentially use the sand to travel, like surfing on it. His relationship with other characters might also change. For instance, Bakugo might be even more envious of this unique quirk. And Izuku would have to learn how to use it subtly, perhaps by creating small sand particles to gather information without being noticed.
A plot for this fanfic could be that Izuku discovers his sand quirk at a crucial moment during a battle. From then on, he starts to train intensively with it. The story could focus on his growth as a hero with this new quirk. He might have to participate in special training sessions designed for quirks like his. There could be a tournament arc where he shows off his new abilities. However, he also has to deal with the fact that some people are skeptical of his sudden change in quirk, and he has to prove himself not only to his enemies but also to those who doubt him.
Well, perhaps a major plot twist could be that Izuku's All for One quirk is actually a modified version created by some secret organization. This organization wants to use Izuku as a weapon. As he uncovers this truth, he has to not only deal with the power of the quirk but also fight against the organization that manipulated him into having it. This would add a whole new layer of mystery and danger to the fanfic.
His relationships with his friends would likely become more complex. If he starts using his time quirk to change things, his friends might not remember the original timeline, but Izuku would. This could create a sense of isolation for him as he holds memories that no one else does.
His relationship with Bakugo might change. Bakugo, who used to look down on Izuku, might now be a bit jealous or even more competitive as Izuku's Dragon Slayer quirk is very powerful. With his friends like Uraraka, she could be in awe of his new quirk and support him more actively in battles. Izuku might also attract the attention of some of the more powerful heroes in training, who want to team up with him because of his unique ability.
His relationship with his teachers could also change. The teachers might be more interested in studying his sentient quirk, which could lead to special training or extra attention. This could either make Izuku feel special or pressured, depending on how the author writes it.
His relationship with Bakugo would be very different. Instead of Bakugo looking down on Izuku for being quirkless, he might be jealous of Izuku's powerful fire quirk. This could lead to even more intense rivalries between them. With All Might, All Might might be more cautious in training Izuku as a fire quirk could be more dangerous to handle without proper control.
Often, the main character would be the one with the stretch quirk. They are usually the focus as they navigate the world of BNHA with their unique ability. There might also be a mentor figure, someone who has more experience with quirks and helps the stretch - quirk character develop their skills. And of course, there could be friends or allies who team up with the stretch - quirk character in battles or adventures.
His relationship with his mother could become more complex. She might be worried about his new nature and try to protect him more. With his friends, like Bakugo, they might initially be scared or distrustful when they find out about his quirk.