The snake might help Harry in his search for Horcruxes. It could use its unique senses to detect the presence of dark magic associated with the Horcruxes. For instance, it could lead Harry to a hidden location where a Horcrux is concealed.
Perhaps the pet snake is actually a transformed wizard who was cursed. As Harry tries to figure out how to break the curse, he and the snake go on a journey. Along the way, they meet different magical creatures who either try to help or hinder their quest to reverse the transformation, and this journey becomes a major part of the fanfiction.
In some fanfictions, the snake could be a magical gift from a mysterious wizard. Maybe it was given to Hermione because she showed great potential in handling magical creatures.
Maybe it's an anonymous gift from someone who has been observing Harry. This person could be a former student of Hogwarts who has a special connection to snakes and sees that Harry has a kind heart and would take good care of the snake. So they leave the snake for Harry to find with a simple note that just says 'For Harry Potter'.
The dragon could help Harry in battles. For instance, in a fight against Voldemort's Death Eaters, the dragon's firepower would be a great advantage.
The snake could help Harry find his way around Hogwarts. You know, Hogwarts is a huge and complex place. The snake might be able to sense the different magical auras of different areas and lead Harry to where he needs to go, like the library when he has to study for an important exam or the Room of Requirement when he's in a tight spot.
Well, it could be that Harry's snake has some magical powers. Maybe it can communicate with other magical creatures secretly. It could help Harry in his adventures, like finding hidden passages or warning him about danger.
In this fanfiction, it could be that the snake is actually a magical creature under some dark spell. Harry, being the brave hero, tries to find a way to break the spell and free the snake from its venomous and aggressive state. He could use his knowledge of potions and magic to figure out a solution. For example, he might recall a particular potion from his studies at Hogwarts that could counteract the venom. And then, through a series of adventures and challenges, he manages to make the snake friendly or at least non - hostile.
Well, the spider could be a very special one. Maybe it's a magical creature that only Harry can understand. They could communicate in a unique way, and the spider could give Harry advice on how to deal with difficult situations at Hogwarts, like when he has problems with Snape or other students. It could also be that the spider is a key to unlocking a hidden part of the castle that holds a great secret.
The girl could take her pet snake to school for show - and - tell. Her classmates might be scared at first, but then become interested as she explains about the snake's habits. Or the snake could escape from its cage and the girl has to search all over the house to find it. Maybe it ends up in the attic or under the bed.
One possible plot could be that the pet snake animagus is actually a reincarnation of an ancient wizard. Harry discovers this when the snake starts showing signs of intelligence and knowledge beyond what a normal snake should have. They form a unique bond and the snake helps Harry understand some of the more obscure parts of magic. The snake could also have enemies from its past life, which now target Harry, leading to a series of adventures where Harry has to protect both himself and the snake while also trying to uncover the snake's true past and how it can help in the fight against the dark forces.
Perhaps the hellhound has a special power like being able to travel through fire unharmed. This power could play a crucial role in the story. For example, the main character and their friends get trapped in a burning building, and the hellhound uses its power to create a path through the fire, allowing them to escape. The fanfiction could then focus on how they keep this power a secret from the school authorities.