Indeed, Wolverine and Sabertooth are considered brothers in the comics. However, their interactions are filled with rivalry and hostility, making their brotherhood a very strained one.
I'm not sure specifically as I haven't read it. But generally, if it's a fanfic about a sabertooth, it might be about Bella's adventures in a world related to sabertooths, perhaps she has some special relationship with them, like befriending a sabertooth or being part of a story where sabertooths play a crucial role.
Sorry, I have no information regarding the author of this particular fanfic. It could be an amateur writer who just shared it on a small fanfic community, or it could be someone more well - known within the sabertooth or relevant fandom, but without further research, there's no way to tell.
Definitely not. Harry Potter has a rich and detailed lore of its own. It follows the adventures of Harry, Hermione, and Ron in a world full of magic, mystery, and danger. Sabertooth fanfiction, on the other hand, would be related to the Sabertooth concept which has no connection to the world of Harry Potter. The magical elements in Harry Potter like the Philosopher's Stone, the Marauder's Map, and the various magical creatures are unique to its own universe and not borrowed from Sabertooth fanfiction.
A common theme is their rivalry. It's often explored in depth, like in 'The Eternal Rivalry' fanfic where their battles are not just physical but also a battle of wills. They constantly try to outdo each other.
In fanfictions like this, the character development of Natsu within the context of Sabertooth is interesting. He could learn new magic techniques from them or teach them his own unique brand of Fairy Tail spirit. It might also explore how the different cultures of the two guilds clash or blend.