Okay, here are the classic Harry Potter sayings:
It's not about who you are, it's about what you do
2 You Can't Connectthe Dots Looking Forward Instead of Backward -Hermione (H)
3 You just can't help but be your own greatest teacher -Ron (L)
The only way to get good at Defense Against Magic is to practice practice -Albus Dumbledore (A)
5 You just have to believe in yourself -Harry (H)
If you want to go fast go alone If you want to go far go together -Dafindo Diggory (D)
You can't change who you are by trying to change who others think you are -Severus Snape (S)
You can't connect the dots looking forward onlybackwards -Bellatrix Lestrand (B)
All you have to do is look forward to the future and you'll know. -Albus Dumbledore
There are no shortcuts to good magic practice -Ron Weasley
One possible reason could be that Dumbledore believes he is acting in Harry's greater good. Maybe he thinks that by taking certain items from Harry, he can protect them from falling into the wrong hands. For example, if Harry has a powerful magical artifact that Voldemort desires, Dumbledore might steal it to keep it safe.
In the fanfiction, Snape could protect Harry from Dumbledore by using his skills in potions. For example, he might create a potion that hides Harry's magical signature from Dumbledore's detection. Or he could use his knowledge of the Dark Arts to counter any spells or charms that Dumbledore might use to keep tabs on Harry. Snape is very intelligent and resourceful, so he could find various ways to physically and magically shield Harry from Dumbledore.
One possible reason could be that Harry is afraid of Snape's intimidating presence. Snape has always been strict and rather unfriendly towards Harry in the original series, so in the fanfiction, this fear might be amplified, causing Harry to run. Another reason could be that Harry has stumbled upon something he shouldn't have seen that involves Snape, and he's running to avoid getting caught.
One possible reason could be that she is in a desperate situation. Maybe she needs something for a very important spell or potion to save someone's life and she thinks Harry won't notice or will forgive her. For example, if there is a rare ingredient that only Harry has access to and time is running out.
Maybe she's desperate for some knowledge that she thinks Harry has in those books. For example, if the books are related to some dark magic or ancient spells that she wants to study for the greater good, she might be tempted to take them without asking.
He might simply stand between Draco and the girls. Harry is quite well - known and respected, so his presence alone could be enough to make the girls back off a bit.
Yes, it can be. It broadens his perspective on his own story. He gets to see how others perceive him and his world. This can give him new insights into his relationships and his role in the wizarding world.
In a large number of fanfictions, Harry is indeed made to be descended from the founders. This concept allows for a great deal of creativity. It could mean that he has an innate understanding of the magic that the founders were known for. Maybe he has a natural affinity for the secrets of Hogwarts if he's related to Helga Hufflepuff, or perhaps he has a more political influence within the wizarding world if his ancestry is linked to Rowena Ravenclaw. Fanfiction writers use this idea to expand on the existing Harry Potter universe in unique and exciting ways.