He might try to prove himself. Naruto could focus on becoming stronger and more successful as a ninja. By showing his family that he can achieve great things and that he's a good person, he hopes to change their minds. For example, he might take on difficult missions and complete them with excellence.
If he asks Hinata, she would probably be overjoyed. She has always been in love with Naruto, so her answer would most likely be an immediate 'yes' with tears of happiness in her eyes.
I'm not entirely sure if there is a specific fanfiction with exactly that premise. However, given the popularity of both Naruto and the concept of sealing powerful entities in Naruto's world, it's quite possible. Fanfiction writers love to experiment with combining different fictional elements, so it wouldn't be surprising if someone has written a story where Jenova is sealed in Naruto. You can try searching on popular fanfiction websites like Fanfiction.net or Archive of Our Own to find out for sure.
Well, Naruto might become more mysterious. Since Gaster is an unknown and rather enigmatic entity, Naruto could start having strange thoughts or powers that he doesn't fully understand at first. He might seem more withdrawn as he tries to figure out what's going on inside him, and his normal cheerful and straightforward personality could be clouded by the presence of Gaster.
One reason could be for power. Combining their strengths through marriage could make them an even more formidable force. Maybe Sasuke saw it as a strategic move to protect their village or to face some greater threat that they are not aware of yet.
His abilities would change in multiple ways. Firstly, his chakra control might be affected. Since Godzilla is a massive and powerful entity, it could disrupt Naruto's normal chakra flow. However, he could also learn to harness Godzilla's power within him. For example, he might be able to use Godzilla's raw strength to enhance his Sage Mode or even his Nine - Tails transformation. This could make him an even more formidable opponent. His speed could also be enhanced as Godzilla's power might give him a boost in his physical capabilities, allowing him to move faster and react quicker in battle.
Naruto would probably be very confused at first. Kushina is his mother, so her hurting him would go against his understanding of their relationship. He might initially try to talk to her, to find out what's wrong and if there's a way to fix it.
In many such fanfictions, it could be a variety of deities. It might be an ancient and powerful god from Naruto's world's mythology that the story's author has chosen to insert. For example, it could be a god of elements like a super - powerful fire god, which could give Naruto even more control over his existing fire - based jutsu and new, more extreme abilities related to fire.
At first, Naruto would likely be very confused and hurt. He has always craved family love and acceptance, so this sudden turn would be a huge blow. He might try to plead with his family, asking them to believe him and give him a chance to explain.