One interesting headcanon could be about the backstories of the Servants. For example, there might be a headcanon that a certain Servant had a secret friendship in their past life that influenced their character in the game. Another could be related to the magic system in the Fate Grand Order universe, like a unique way of casting spells that isn't shown in the main story.
Well, a popular headcanon is that Percy can see the memories of the ocean. So in fanfiction, he might touch an old piece of coral and suddenly be flooded with images of ancient sea battles or long - lost civilizations. Also, some think that Annabeth has a fear of heights that she hides really well because she doesn't want to seem weak. As for Grover, perhaps he has a family of satyrs in a hidden grove that he secretly visits and they tell him old satyr tales that he then uses to his advantage on quests.
I like the headcanon where Annabeth is a master of disguise. In fanfiction, she can blend into any crowd, not just because of her intelligence but also because she has some magical items that help her change her appearance. It makes her even more resourceful on quests. Grover, on the other hand, has a headcanon where he can grow plants with just a touch. So if they're in a barren area, he can create a little oasis for them to rest in. This shows his connection to nature in a more powerful way.
One idea could be that Neville Longbottom is secretly a powerful wizard all along but has been suppressing his power due to self - doubt. Another could be that the Hogwarts portraits have their own little society and gossip network within the castle walls. And a third one might be that Hagrid has a secret family of magical creatures in the Forbidden Forest that he takes care of.
It can add more depth to minor characters. For example, by creating headcanons about characters like Lavender Brown, we get to see a side of the Hogwarts student body that wasn't fully explored in the original. It gives them more personality and backstory.
Deadpool became Deadpool through a series of complex and sometimes convoluted events in the comics. He was originally a mercenary named Wade Wilson, who underwent experimental treatments that gave him his unique powers and personality.