In some fanfics, there could be a magical creature or spirit that Mundungus has befriended in the past. This creature or spirit, being loyal to him, might try to help him in some way. It could be a house - elf that he once helped, and now the house - elf wants to return the favor. Or it could be a magical bird that can carry messages and tries to find someone to assist Mundungus in his predicament.
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.
Perhaps it was because of the power he amassed in the process of defeating Voldemort. In the fanfic world, power can be a very scary thing to those in authority. Harry's new - found and possibly overwhelming power could have made the existing magical power structure feel threatened. So, they arrested him as a way to control and contain that power, rather than seeing him as a hero who saved the wizarding world.
One common theme is redemption. Mundungus is often depicted as a rather unlikable character in the original series, so in fanfiction, he's often on a path to redeem himself, with Hermione sometimes being the catalyst for that change.
Maybe Harry accidentally frames Weasley for something. It could be due to a misunderstanding, like a spell gone wrong that makes it seem like Weasley was involved in some illegal magic use.
Well, in fanfiction, anything can happen. Regarding Dumbledore stealing from Harry, it depends on the specific fanfic. Some might show Dumbledore stealing Harry's inheritance, perhaps believing he can use it for a greater good. But this is not in line with the general perception of Dumbledore in the main series. Fanfic writers like to twist and turn the characters to create new and interesting stories.
One possible scenario in such a fanfic could be that Draco steals a potion to gain an advantage in a wizarding duel. Maybe he's desperate to prove himself against Harry Potter and thinks the potion will give him an edge, like a strength - enhancing or a quick - thinking potion.
Maybe it's a corrupt Ministry of Magic official. They might use Harry's credibility to their advantage and trick him into providing false information about Weasley. They could be after the Weasley family for political reasons or because they want to cover up their own misdeeds by creating a distraction with Weasley's arrest.
In the fanfic, it could be that Snape is caught in a political struggle within the wizarding world. Harry, who is on the side of the 'good' political faction, uncovers Snape's involvement in some underhanded schemes for the opposing side. As a result, he has no choice but to get Snape arrested to protect the safety and stability of the wizarding community.