Yes, there are quite a few. You can find them on various fanfiction websites. Some might focus on crossovers of the characters, like how the Servants from 'Fate Stay Night' would interact with the vampires in 'Hellsing'.
There are indeed some great ones. For example, some fanfictions might explore the concept of the Holy Grail from 'Fate Stay Night' being involved in the vampire - hunter world of 'Hellsing'. They often bring new and exciting storylines by combining the unique elements of both franchises.
One common theme is the clash of different power structures. The magic and Servants of 'Fate Stay Night' against the vampiric powers in 'Hellsing'.
Sure. In some fanfictions, the gamer theme is blended with the Fate/stay night lore. There might be a story where a group of gamers discovers a way to enter the Fate/stay night world and they start to compete not just for the Holy Grail but also to prove their gaming superiority within this new and dangerous realm. They might encounter different Servants and Masters and form unexpected partnerships or rivalries.
One interesting concept could be the crossover of the power systems. For example, how would a Quincy from 'Bleach' fare against a Servant's Noble Phantasm in 'Fate Stay Night'. Another concept might be the character interactions. Picture Ichigo from 'Bleach' having a conversation with Shirou from 'Fate Stay Night' about their respective ideals of justice and protecting others. Also, the different magical and spiritual realms in both universes could merge in unique ways in the fanfiction, like the Soul Society and the Throne of Heroes interacting in some unforeseen manner.
There is also 'In the Company of Archer and Rin'. This fanfiction focuses on their daily lives together after the events of the main story. It shows how they support each other, from Archer's combat advice to Rin's magical knowledge sharing. It's a heartwarming read that delves into their characters.
Yes, there are many. Some focus on exploring Dark Saber's backstory in the Fate Stay Night universe. For example, there are fanfictions that delve into her origin as a corrupted version of Saber. These stories often add new dimensions to her character.
One interesting Fate Stay Night Naruto fanfic is 'Naruto in the World of Fate'. In this fic, Naruto is somehow transported to the Fate Stay Night universe. It's really cool to see how his ninja skills interact with the magic and combat system in the Fate world. Another one could be 'Fate Servants in Konoha' which imagines what would happen if Fate's Servants showed up in Naruto's village.
Sure, there are many out there. The beauty of fanfics for this pairing is that it gives writers the freedom to play with different ideas. In some fanfics, the relationship between Jeanne and Shirou might be more of a slow - burn type. They start as acquaintances, gradually getting to know each other better. Writers might also add in elements from different Fate series to enrich the story, like including concepts from Fate/Grand Order in the fanfic about Jeanne and Shirou's relationship.
The concept of Danny's ghostly abilities meshing with the magic of the Fate universe is really interesting. His powers, like intangibility and flight, could give him an edge in battles against Servants. For example, he could use his intangibility to avoid attacks that would normally be deadly.
One interesting crossover could be the magic systems interacting. In 'Harry Potter', magic is more about spells and potions, while in 'Fate Stay Night', it's linked to Servants and their powers. Maybe a scenario where a Harry Potter character tries to summon a Servant. Another could be the characters' moral compasses clashing or aligning. For example, how would Harry Potter deal with the often morally gray situations in the 'Fate Stay Night' universe? And of course, there could be crossovers in the settings, like Hogwarts being a battleground for a Holy Grail War.
One interesting idea could be exploring different routes for the characters. For example, what if Shirou had chosen a different Servant at the start? Another could be delving deeper into the backstories of the Servants, like revealing more about their lives before they became heroic spirits. Some fanfictions also play with the concept of alternate universes, where the rules of the Holy Grail War are changed completely.