He might introduce more fair lending practices. In the wizarding world, some families or individuals might have been unfairly treated when it comes to borrowing money from the bank. Harry could change that.
The characters would first need to identify the robbers. Harry Potter has his Invisibility Cloak, so he could use it to spy on the robbers and find out their plans. Once they know what's going on, they'd gather their allies. Dumbledore, if he were still alive in the fanfiction, would offer his wisdom and powerful magic. The trio - Harry, Hermione, and Ron - would then work together with other Hogwarts students or members of the Order of the Phoenix. They might set up magical traps around the bank to catch the robbers or use spells to immobilize them when they make their move.
One possible plot could be that a group of dark wizards, inspired by Muggle bank robbers, plan to rob Gringotts. They use dark magic to bypass the goblin security and try to steal valuable magical artifacts stored there. Harry Potter, along with his friends, gets wind of this and decides to stop them. They use their own magic skills and knowledge of the wizarding world to outwit the robbers.
They could be used to create a mystery. Say a set of bank statements has some encrypted or missing information. Harry and Hermione would use their knowledge of magic and codes to try and decipher it, leading them to a secret vault or a hidden treasure.
One possible plotline could be that the bank statements reveal some secret transactions related to the dark arts. Maybe a character has been secretly buying dark artifacts and the discovery of this through the bank statements sets off a whole new adventure to stop a potential dark plot. Another could be that the statements show that a character has been misusing their family fortune and this causes a rift within the family, like if a Weasley was found to be using the family funds inappropriately.
No. Bank robbery stories usually revolve around the criminal act itself, the motives like financial desperation or greed, and the efforts to catch the robbers. There is no place for sex in such legitimate and serious accounts.
Grave Robber's Chronicles and Harry Potter were two different novel series without a direct thread. Grave Robber's Chronicles was a Chinese web novel that told the story of a group of grave robbers searching for treasures in ancient Chinese tombs. Harry Potter is a series of English magical novels about a group of young people who study magic at Hogwarts School of Witchcraft and Wizardry.
There are no appropriate bank robber stories related to sex. Bank robbery is a serious crime, and we should be discussing it in the context of law enforcement, security, and the prevention of such illegal activities.