A vampire hunter could be a key character. They might initially see Harry as a target too because of his association with the vampire. This would create a lot of tension as Harry and his mate have to either convince the hunter that they are not a threat or fight against them. And don't forget about Dumbledore (assuming this is in the Harry Potter universe). His reaction to Harry's new situation would be very interesting to explore.
Harry is surely a main character. As for the mutant, it could be a mutant with powers like telepathy or super strength. If it's a crossover fanfiction, it might be a popular mutant like Wolverine or Jean Grey. However, in an original take, the mutant could be a completely new character with unique powers and a backstory that ties in with Harry's story in interesting ways.
Hermione could be one. She might use her vast knowledge of magic to help Harry figure out how to hatch the egg. Another could be Hagrid. He has a lot of experience with magical creatures, so he could offer advice on taking care of the egg and the soon - to - be - hatched creature.
Hermione and Ron would also be important characters. Hermione might be initially skeptical of Harry's newfound obsession with the Marauders. Ron, on the other hand, might be more easily swayed and join Harry in his attempts to be more like the Marauders.
There could be his drill sergeant. A tough but fair character who pushes Harry to his limits. Maybe he has a name like Sergeant Thompson.
Well, in some cases, there could be minor characters from the original series who still interact with Harry on a limited basis. For example, Neville Longbottom might make an appearance. Even though Harry is alone for the most part, Neville could cross paths with him and have a brief conversation or exchange that has an impact on Harry's journey.
There could be Ron. He might be Harry's sidekick in the gambling adventures, either joining him in bets or trying to stop him when things get out of hand. Ron's loyalty would play a big part in their relationship within the story.
Ron might also be a main character. He could be initially skeptical of Harry's new powers but eventually come around and support him. He might even use his own skills, like his chess - playing strategy, to help Harry in battles or challenges related to his Dragonborn status.
Ron could also be a main character. He might initially be a bit confused or even jealous of Harry's new powers as an elf, but then come around to support him. His family, like the Weasleys, could also be involved, perhaps providing a different perspective on elves compared to the pure - blood wizarding families.
It's hard to say for sure without reading the fanfiction, but it's likely that Ron and Hermione are still important characters. They are Harry's closest friends in the original series, and their relationships with a prodigy - Harry would be interesting to explore. Maybe they have to deal with feeling overshadowed by Harry's new - found prodigious abilities.
There could be a wise old teddy bear that acts as a mentor to Harry. It might have been in the toy house for a long time and knows all its secrets.