Often, original characters are added. For example, a new student who has some special ability related to water or swimming. They might befriend Harry and help him in the second task, either knowingly or unknowingly.
One interesting plot twist could be that instead of rescuing Ron, Harry has to rescue a different person who was secretly important to him all along, like Neville. It changes the dynamic as Neville might have different skills or knowledge that Harry has to utilize to complete the task.
One possible fanfic could be where Luna is an unexpected helper in the second task. Maybe she uses her unique perspective and knowledge of magical creatures to guide Harry in some way. For example, she might know a special spell to communicate with the merpeople, which she shares with Harry, giving him an edge in the task.
Harry Potter himself is often a central character in these fanfictions. Since he was the one who originally faced the dragon task in the Triwizard Tournament, many fanfic authors like to explore different scenarios with him in the same situation.
The golden egg is almost always a crucial part of the fanfic's first task. It's not just a goal for Harry to reach, but it often holds some mystery or special power. Some fanfics might even expand on what the egg does or represents beyond what was in the original story. Maybe it has a connection to an ancient magic that Harry has to discover in order to complete the Triwizard Tournament successfully.
Maybe Dobby could be an unexpected ally. He could use his magic to create distractions for the other contestants or help Harry find a hidden passage in the maze. Another possibility is that one of the Hogwarts ghosts, like Nearly Headless Nick, decides to assist Harry. He could float through walls and spy on the other champions' movements and relay the information to Harry.
One possibility could be that Harry, as a Dragon Animagus, uses his new form to his advantage in the First Task. He might be able to outmaneuver the real dragon more easily, flying around it and confusing it. This would give him an edge in retrieving the golden egg.
In some fanfictions, Harry might struggle with PTSD after the third task. The trauma of facing Voldemort again could haunt him, causing nightmares and making him more withdrawn. He might also become more determined to defeat Voldemort, spending all his spare time studying dark magic defenses.
One interesting plot could be a character having to train a dragon for the task in a completely new way, using magic that was previously undiscovered. This would add an element of mystery and innovation to the story.
Well, in a fanfiction of the Harry Potter first task, Harry could find out that the dragons have been enchanted by a dark wizard who wants him to fail. So, he has to not only deal with the dragons but also break the enchantment. Or perhaps Harry has a premonition about the task in his dreams, and with the help of Dumbledore, he learns how to use this new - found ability to his advantage during the task. Also, a fun idea could be that Neville gives Harry a magical plant that can temporarily paralyze the dragon, but Harry has to figure out how to use it correctly in the heat of the moment.