In the fanfic, Naruto could develop a deeper sense of family values. He grew up without parents, so having his own family would make him cherish it even more. Hinata would develop a stronger voice in the family. She might be the one to make important decisions regarding the baby's upbringing, like what kind of education the baby should have.
Naruto would likely become more responsible. He's used to being the hero, but now he has to be a father too. So he might cut back on some of his risky adventures to be there for his family. Hinata would become more confident as a mother. She's always been a bit shy, but with a baby to protect, she'd find her inner strength.
Naruto would probably learn to be more patient. Babies can be fussy, and Naruto, who is used to action - packed situations, would have to adapt. Hinata, she might develop new friendships with other mothers in the village. She could share parenting tips and in the process, become more involved in the community life of the Hidden Leaf Village.
Their relationship would likely deepen. They would have more private time together, sharing their dreams and fears at night. Naruto would become more protective of Hinata in their shared home.
Naruto's character could develop a greater sense of responsibility towards Hinata and her family. Saving her mom would make him more aware of the importance of family bonds, which could in turn influence his own views on his family and his place in the village.
Hinata's family would also have to deal with the emotional aspect. They love Hinata in her normal state, and now they have to adjust to this new form. They might start to remember when Hinata was actually a baby before and all the hopes and dreams they had for her then. Some of the more conservative members of the family might be more hesitant to let Naruto be around her, but the more open - minded ones could see that Naruto's presence is actually good for her in this state. And they would all be united in their goal to get Hinata back to her normal self.
Hinata would be overjoyed. She has loved Naruto for a long time, so his proposal would be like a dream come true for her. She might start crying tears of happiness and immediately say yes without hesitation.
It could start with Hinata being more open about her admiration for Naruto. Instead of just blushing and being shy, she starts to actively engage with him as a friend. Naruto, being Naruto, would be very accepting and they'd start hanging out. For example, they could share ramen together, which is Naruto's favorite. This simple act of sharing food could be the start of a deeper connection.
The baby might inherit Naruto's ability to use chakra in large amounts and his signature Rasengan. Since Naruto has such a vast amount of chakra, it's likely that his child would also have a significant chakra reserve.
For Naruto, you can show his more romantic and sensitive side. He could be more attentive to Hinata's feelings and needs. For example, he might bring her flowers just because. Hinata can be developed by showing her becoming more confident in the relationship. She could start to initiate dates or activities.
Their relationship could develop through shared experiences. For instance, they might volunteer together to help the orphaned children in the village. This would bring them closer as they both have a soft spot for kids. Naruto, being an orphan himself, and Hinata, who is very nurturing.
Hinata would develop more leadership qualities. With Naruto gone, she realizes that someone needs to step up and be a symbol of hope for those who still believe in Naruto. This would make her more confident in making decisions for the greater good of the village and its relationship with Naruto when he returns.
The training could begin as a form of self - defense. Given Naruto's history of facing many enemies, he would want his child to be able to protect itself. He and Hinata might start by teaching the baby how to sense danger. They could use games, like hiding and seeking with a 'dangerous' element added. For example, Naruto would create a harmless clone that the baby has to detect and avoid. This would help the baby develop both its sensing abilities and its reflexes.