Well, Bellatrix would face the challenge of dealing with Harry's connection to Dumbledore and the Order of the Phoenix. Harry would constantly be thinking about his allies, and Bellatrix would have to find a way to break that connection. Moreover, she would have to teach Harry the Dark Arts without accidentally triggering his natural inclination towards the light. It's like trying to force a square peg into a round hole. And she also has to make sure Harry doesn't escape and expose her actions to Voldemort or other Death Eaters.
One challenge would be Harry's strong will. He has his own beliefs and values that are opposed to Bellatrix's dark ideology. Another challenge could be hiding Harry from Voldemort. Voldemort might not approve of Bellatrix raising Harry in her own way. Also, Bellatrix herself has a reputation to uphold among the Death Eaters, and raising Harry could be seen as a risky and strange move.
In a fanfic, Bellatrix would first face the challenge of gaining Harry's trust. Since she is a known Death Eater, Harry would be naturally distrustful of her. Then, she has to deal with the magical world's perception of her actions. The wizarding community would not look kindly on Bellatrix raising Harry. Additionally, she would struggle with Harry's Gryffindor courage. Harry would not be easily intimidated, and he would constantly fight against Bellatrix's attempts to make him embrace the Dark Arts. This would create a constant battle of wills between them.
One major challenge would be understanding the magical world. Tony Stark is a man of science, and magic operates on very different principles. He'd have to learn about spells, potions, and magical creatures. Another challenge could be dealing with the wizarding community. They have their own traditions and laws, and Stark might find it difficult to fit in or make sure Harry follows all the rules. Also, protecting Harry from magical threats might be tough for Stark as his technology might not always work against magic.
One challenge could be Naruto's impulsive nature. He often rushes into things without thinking, and Tsunade would have to find a way to rein him in. Another might be dealing with Naruto's fame. Since he is the Jinchuriki of the Nine - Tails, he has a lot of attention on him, and Tsunade would need to protect him from those who might want to use or harm him.
One challenge could be the public perception. The wizarding world may not be very accepting of Hermione raising Voldemort's daughter. There could be a lot of fear and suspicion. Another challenge is Delphini's own nature. Since she has Voldemort's blood, she might have some inborn dark tendencies that Hermione has to constantly fight against. Also, Hermione would have to deal with the memories and legacy of Voldemort that might be a part of Delphini's upbringing.
One challenge Naruto might face is Gaara's past traumas. Gaara has been through a lot of pain and isolation, which has made him distrustful. It would be difficult for Naruto to break through those barriers and get Gaara to open up. Another challenge could be the political situation. Suna and Konoha have had their differences in the past, and some in Suna might not be happy with Naruto's influence on Gaara. Naruto would have to deal with any potential political unrest or opposition from those who don't trust Konoha.
One challenge could be time management. The adventurer has to balance exciting and often dangerous adventures with the daily routines of parenting like school runs and meal times. For example, if they are called away on a sudden adventure, they might have to quickly arrange for someone to look after the kids.
They might face social challenges. In the wizarding world, there could be those who don't approve of their relationship or their decision to raise a child together. Also, financial challenges could arise. Even though they are heroes, they still need to provide for the child's needs, like education at Hogwarts which might have costs associated with it.
Another challenge would be the level of power they start at. Gohan has extremely high power levels as a Saiyan, especially if he has access to his Super Saiyan forms. Naruto, while very powerful in his own right, might find it hard to keep up at first. This could lead to feelings of inadequacy on Naruto's part and pressure on Gohan to not accidentally harm Naruto during training.
One challenge would be dealing with his natural inclination towards power. Tom Riddle has always been power - hungry, and Fem Harry Potter would have to constantly find ways to redirect this drive in a positive way. For instance, she might encourage him to use his power for the good of the wizarding community.
One challenge could be dealing with their different personalities. Each sibling might have their own desires and goals. For instance, one might be more interested in military matters while another in the arts. Rhaenyra would have to find a way to nurture all of them individually.
In the fanfiction, Kakashi might face the challenge of Naruto's insecurities. Naruto has always had a complex about being alone and not having a family. Kakashi would have to find ways to make Naruto feel secure and loved. Also, dealing with Naruto's powerful and sometimes uncontrollable chakra could be a problem. Kakashi would need to train Naruto to master his chakra properly without it overwhelming him.