The pet might cause trouble for Harry. Imagine it has a mischievous streak and keeps getting into places it shouldn't be, like the Slytherin common room. This would lead to all sorts of awkward and dangerous situations for Harry, forcing him to come up with creative solutions to get out of trouble.
In fanfiction, Harry's unusual pet could also bring new friendships. If it has some rare and valuable abilities, other students or even teachers might be interested in it. This could lead to Harry interacting with people he wouldn't normally interact with, changing the social dynamics at Hogwarts and thus affecting the overall plot.
If the familiar is something like a dragon, it could greatly impact the plot. Dragons are powerful and feared. The character with the dragon familiar might be constantly hunted by those who want to use the dragon for their own purposes or those who fear its power. This would create a lot of conflict and drive the story forward as the character has to protect their dragon and themselves.
The pet bat could make Harry's life more interesting. It could be his companion during lonely times, like when he's in his dormitory and the others are asleep.
Let's say his pet is a dementor. It would change the whole atmosphere of the story. The characters would constantly be in fear of having their souls sucked out. It could also be used to guard important places. For instance, Voldemort might place it near the entrance of his lair. This would make it extremely difficult for the heroes to approach as they have to deal with this terrifying creature first. Also, it could spread a sense of despair among the wizarding community, making people more vulnerable to Voldemort's control.
The protective brother can change the plot significantly. For instance, if he's highly skilled in magic, he can prevent Harry from getting into some of the dangerous situations he faces in the original series. He might be able to stop Harry from entering the Triwizard Tournament by interfering with the Goblet of Fire's magic. This would then change the entire course of that year at Hogwarts and Harry's relationship with Cedric Diggory and others.
It can create immediate conflict. If a young wizard performs magic accidentally, the Trace can bring the Ministry's attention, like in some fanfics where a minor character's small magic act sets off a chain of events because the Ministry gets involved.
The 'darkness' can make the plot more complex. It might introduce new challenges for the characters that they have to overcome. For example, if there are new dark spells or dark creatures in the fanfiction, the characters need to find ways to deal with them.
His anger could drive him to take risks he wouldn't normally take. Maybe he decides to go after a powerful enemy on his own without proper backup because he's so angry that he doesn't think clearly. This could put him in great danger and also change the course of the story as the other characters then have to scramble to save him.
The dog could provide Harry with unconditional love and companionship. In the often - lonely world of Hogwarts where he has so many secrets and enemies, the dog would be a constant friend. It could also help him relax, like when he's stressed about exams or Voldemort.
The concept of Harry as a pyromancer can change the fanfiction plot in many ways. Firstly, his battles would be different. He could use fire to his advantage, which might make him more of a force to be reckoned with. Secondly, his relationships with other characters could shift. Some might be jealous of his new power, while others could be more drawn to him. Also, it could introduce new elements to the overall story, like a search for the origin of his pyromancy powers or a need to control them better to avoid causing accidental destruction.
Well, in many Harry Potter fanfictions with time travel, it can completely change the plot. For example, if a character goes back in time and warns Harry about certain events before they happen. It might prevent some tragedies or create new situations. Maybe they could stop Cedric's death by changing the events in the Triwizard Tournament. This adds a whole new layer of complexity and excitement to the story.