Maybe a 'Fire Illusion' spell. Using her fire powers, she could create illusions made of fire. This could be used to distract enemies or create false paths in a maze - like situation. For example, in the Triwizard Tournament maze, she could have used this to mislead the other competitors.
Well, one spell he might create is 'Ice - Levitate'. This spell would allow him to levitate ice - made objects or even frozen enemies. Also, a spell called 'Arctic - Blast' could be developed. It would send out a powerful blast of ice and cold air that could knock back multiple enemies at once. He could also come up with a 'Cryo - Vision' spell, which gives him the ability to see through ice or in icy conditions more clearly than normal, useful for finding hidden things in ice caves or frozen lakes around Hogwarts.
One common power she might be given is telekinesis. This allows her to move objects with her mind, which could be really useful in various situations in the fanfiction world, like during battles or when she needs to retrieve something out of reach. Another power could be enhanced intelligence, beyond what she already has in the original story. This would make her an even greater force to be reckoned with when it comes to solving complex magical problems or outwitting her enemies.
Hermione could be into nature - inspired tattoo styles. Since she loves books and knowledge, she might design tattoos of magical plants like the Whomping Willow or the Mandrake. These tattoos could have a touch of magic where they seem to sway or make sounds like the real plants in certain situations.
One spell she could teach is a charm for protecting books from any kind of damage. Given Hermione's love for books, this would be a great addition to the curriculum. Also, a spell for magically highlighting important parts of textbooks as you read them would be very useful. This spell could be activated by just thinking about the relevant information while reading.
One spell Harry could create is a 'Lumos Maximus Amplificatus' which would create an extremely bright and long - lasting light, much stronger than the regular Lumos spell. This could be useful in very dark and dangerous places like the Forbidden Forest at night.
There could be a spell named 'Silk - Shield'. Harry, with his spider - like abilities, might come up with a spell that creates a shield made of magical silk. The silk could be as strong as the real webs spiders make, but also have magical properties. For example, it could be enchanted to absorb dark magic. Additionally, a 'Spider - Grip' spell could be developed. This spell would give the caster the ability to hold onto things as tightly as a spider holds onto its prey or its web, which would be useful in many dangerous situations.
She could have the power to control water, of course. This means she could make water move in any way she likes, like creating waves or even making water spouts. She might also be able to breathe underwater without the need for spells like the Bubble - Head Charm. Another power could be the ability to communicate with sea creatures, which would be really cool. She could ask for help from whales or dolphins, for instance.
Perhaps she has the power of mind control. In the fanfiction, she might be able to influence the thoughts and actions of others, which could be really useful in various situations. For example, she could make an enemy vampire stop attacking her friends by simply using her mind control power.
Perhaps a story where Naruto's fire powers are not fully under his control at the start. He accidentally sets things on fire and has to go on a journey to learn how to master them. Along the way, he meets an old sage who teaches him unique techniques related to his fire powers.
To create spells in Harry Potter fanfiction, you need to be creative. Think about the wizarding world's rules. Spells are often related to a particular wand movement as well. If you want to create a spell for levitating small objects, you could call it 'Levitio Minimus'. For the incantation, make it something that rolls off the tongue easily. Maybe it has a rhyme or a rhythm. You can also draw inspiration from nature. A spell for making plants grow could be 'Flora Cresco'.