Harry Potter's friends in fanfiction vary a great deal. There are the international friends. Since Hogwarts is a British school but the wizarding world is global, in fanfiction, he could have friends from other magical schools around the world. These friends would bring in different magical cultures and techniques. Also, there are the friends who are from different time periods. Some fanfictions might introduce time - travel elements, and Harry could befriend wizards or witches from the past or future. His relationships with these friends can be complex, as they have different values and ways of life based on their time of origin.
One of his friends could be a young werewolf who is struggling to control his condition. Harry, having faced his own challenges, would befriend him and help him find a way to live a more normal life in the wizarding world.
One possible storyline could be Harry making friends with students from different houses at Hogwarts. For example, he befriends a shy Ravenclaw who helps him with his studies in a unique way. Another could be Harry befriending magical creatures, like a friendly centaur who gives him advice on dealing with the Forbidden Forest.
It could be that he is wrongly perceived as dangerous. After all, he has survived the Killing Curse as a baby and Voldemort is always after him. People might be afraid to get close to him for fear of getting caught up in the dark wizard's wrath.
He might focus on his studies. In the wizarding world, there are so many interesting magical subjects like Potions, Transfiguration. By burying himself in books and learning new spells, he can at least distract himself from the lack of friends.
It could be from a far - off land. Maybe it was crafted by a reclusive wizard in a distant mountain range. This wizard might have used unique materials and spells to create it, and for some reason, the wand made its way into Harry's hands.
Well, different 'want' in Harry Potter fanfiction could mean different things. One aspect is the want for adventure. Many fanfictions explore characters' desires to go on new adventures outside of Hogwarts. Another could be the want for acceptance. A character might be an outcast in the original story but in fanfiction, they strive for acceptance within the wizarding community. Also, there's the want for revenge, which can create really intense storylines in fanfiction where a character has been wronged and wants to get back at those who did them harm.
The different wand might change his abilities in terms of spell specialization. Say the new wand has a different wood that is attuned to certain types of magic. If it's a wand made of willow, which is often associated with healing magic, he could find himself more proficient in healing spells, even if he wasn't before. This would be a significant shift in his magical abilities as he would be able to contribute in a different area of magic within the wizarding world.
One idea could be that Harry's new father is a powerful wizard from a different magical society. This could introduce new types of magic and cultures into the story.
His friends might be initially very confused about his dual heritage. They could be both in awe and a bit intimidated by his connection to Hawkeye. For example, Ron might be a bit jealous at first because Harry has this really cool non - wizarding connection on top of being a famous wizard. Hermione, on the other hand, would be very interested in researching how such a connection could even be possible and would try to find historical precedents.