In this fanfiction, it's possible that some of the professors from Hogwarts get involved. Professor McGonagall could be worried about Harry going fishing and might send a spell to protect him. Professor Snape, on the other hand, might think it's a waste of time and try to stop Harry, but then get roped into the adventure somehow when he realizes there might be some valuable potion ingredients in the fish Harry is trying to catch.
There could be some new characters created specifically for this fanfiction. For example, an old wizard who lives near the fishing area and gives Harry some tips on magical fishing. Or perhaps a mermaid who tries to play tricks on Harry while he's fishing. Hagrid might also be involved, as he loves all kinds of magical creatures and fishing could be a new adventure for him too. He could bring along some of his strange pets to the fishing trip.
Obviously, Harry Potter himself is the central character. Hermione and Ron would most likely be involved too. They would probably try to find a way to get Harry out of Azkaban. Dumbledore might also play a role, perhaps guiding Hermione and Ron from behind the scenes or even trying to influence the wizarding court to re - evaluate Harry's case.
In this fanfiction, Harry might use magic to catch some really strange and magical fish. Maybe he'll encounter magical creatures while fishing in a hidden lake at Hogwarts.
Voldemort would surely be involved. He might initially be suspicious of Harry's sudden change but then see it as an opportunity to use Harry's power for his own dark ends. He could try to mentor Harry in the ways of dark magic.
In this fanfiction, Neville could also play a role. He has grown into a brave and capable wizard. He might use his skills with plants to create some sort of magical plants that could help, like plants that can grow quickly to block the path of the iceberg or to repair any damage to the ship. And Luna could be there with her unique perspective, perhaps she could sense the danger in a different way and help Harry in his mission to save the Titanic.
Ron could be there too. He might be more interested in the cool features of the cars, like the sound systems or the design. He could be the one who tries to convince Harry to add some fun elements to the cars they work on. And Hagrid might also show up, being all amazed by these strange Muggle contraptions and accidentally breaking something while trying to figure out how they work.
Neville could be in it too. He might be initially shocked to see Harry in such a state but then tries to help by using some of his herbology knowledge to make a potion to counteract the drunkenness. And Malfoy could show up, taking the opportunity to mock Harry until Harry, in his drunken craziness, does something that scares Malfoy off. Also, Hagrid would surely be around, being concerned about Harry and trying to get him to rest in his hut.
Obviously, Harry Potter himself would be the central character as the title implies. Hermione and Ron would most likely be involved as well, since they are Harry's closest friends. They would probably be the ones trying to figure out what's wrong with Harry and how to fix him. Dumbledore could also play a big role, as he often has the wisdom and power to deal with strange situations.
Dumbledore could make an appearance. He might be the one who gives Harry the idea to become a pilot in the first place or provides some ancient magical knowledge about flying that helps Harry in his new career. Also, the Weasley twins could be involved. They could create some magical gadgets for the plane, like a device that makes the plane do cool stunts.
Hermione could be involved. She might be the one who comes to check on Harry because he's been in the shower for a long time. She could be worried that something's wrong, like if a dark spell has been cast on him. And when she knocks on the door, Harry has to quickly figure out how to respond while still being in the shower.
Neville Longbottom can also be a main character in some 'Harry Potter goes back in time' fanfictions. Given his growth and importance in the original series, in the fanfic, Harry might go back and help Neville become more confident earlier. This could have a significant impact on the fight against Voldemort as Neville could then be an even more powerful ally from an earlier time.