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 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.
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.
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.
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.
Financial difficulties could also be a problem. Naruto might not be well - off initially, and raising a child requires money for things like food, clothes, and education. He would have to find ways to provide for his sister while still being a ninja. Also, there could be threats from Naruto's enemies who might try to target his sister to get to him.
He'd first need to deal with the food problem. Chimeras might need a special diet, so Harry would probably have to do some research or ask Hagrid. He'd also need to make sure the chimera doesn't harm other students or creatures at Hogwarts. He might use magic to create a safe space for it. And when it comes to training, he'd have to be patient and use positive reinforcement.
Another challenge would be his changed appearance. His fangs and pale complexion could make it difficult for him to blend in at Hogwarts. He might be ostracized by some students and even some teachers. His vampiric abilities, while useful in some ways, could also be a hindrance as he tries to maintain his normal wizard life. For instance, his sensitivity to sunlight could limit his outdoor activities during the day.
In a fanfic, Harry as a girl would face the challenge of re - defining her identity. She has been known as a male hero, and now she has to create a new image for herself. This could be difficult in the wizarding community where reputations are important. She would also have to adapt to the physical differences, like having a different body structure for dueling or flying on a broomstick, which could take time to get used to.