Sasuke might face the challenge of understanding baby Naruto's needs. Since he's not used to dealing with infants, things like feeding, changing diapers could be really difficult for him.
One big challenge would be protecting baby Naruto from those who might want to harm him. Sasuke has his own enemies, and they could target Naruto to get to him. Also, Sasuke has to deal with the fact that he's not very good at showing emotions, but he needs to be affectionate towards baby Naruto to help him grow in a healthy way.
They could face challenges from the ninja world's authorities who might see them as deserters. Other villages might try to capture them to gain an advantage over Konoha.
Naruto would face quite a few challenges. For one, his growth might be stunted as the team overprotects him. He could also face ridicule from outside the team who might see him as a weakling now. Moreover, he has to deal with the internal team dynamics where Sasuke may not be fully accepting of his new role and Naruto would have to prove himself constantly.
One challenge could be communication. If they come from different backgrounds or cultures within the fanfic world, they might have trouble understanding each other at first. For example, if Sayo Hitsugi has a very formal and traditional way of speaking and Naruto is his usual brash self. Another challenge could be trust. Naruto has been betrayed before, so he might be hesitant to trust Sayo Hitsugi right away, and vice versa. They would need to overcome this to work together effectively.
One challenge Naruto might face is Sasuke's own will. Sasuke may be so consumed by his thirst for revenge or his dark path that he doesn't want to be brought back. Naruto has to break through that mental barrier. Another challenge could be the external forces that are influencing Sasuke, like the people or organizations that have turned him to the dark side. Naruto has to deal with them as well.
In a fanfiction, after their wedding, Sasuke and Female Naruto might face the challenge of balancing their duties. Naruto might want to focus on village improvements while Sasuke may be more interested in security matters. This difference in priorities could lead to arguments. Also, Sasuke has a dark past that still haunts him at times. His nightmares could potentially affect their relationship. Moreover, they will have to deal with the expectations of the village. People will look up to them as a couple, and any mistake they make could be highly scrutinized, adding stress to their married life.
One challenge would be time management. They are both busy shinobi. Naruto has his Hokage duties and Sasuke is often away on missions. Finding time to take care of the baby would be tough.
He might face powerful enemies. For example, if the enemies are from a secret organization with strong and unknown jutsu, Naruto would have to quickly figure out their weaknesses. This could be difficult as he has no prior knowledge of them.
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.
Well, they could face challenges related to their past. They were on opposite sides during the war, and that could create some underlying tensions. Hermione might worry that Draco's old prejudices could resurface, and Draco might be concerned that Hermione will hold his past against him when it comes to raising their child. Additionally, there's the matter of family support. Hermione's Muggle parents may have a hard time understanding the wizarding world aspects of raising a magical child, and Draco's family might not be fully on board either.
Societal prejudice would be a major challenge. The wizarding world has long - held views about blood purity and the divide between those who fought for the light and those who were on the dark side. Hermione and Antonin having a baby together would go against these traditional views. They would have to face a lot of criticism and judgment from the wider wizarding community. Also, there could be challenges in terms of raising the baby with different magical cultures. Hermione is from a more academic and light - magic - based background, while Antonin has his own history with dark magic, and they would need to find a way to blend these for the baby's upbringing.