In such a fanfiction, the plot might involve Naruto turning 'dark' due to feelings of abandonment. He could become bitter and start to question the values Jiraiya taught him. Maybe he'd start using his powers in more ruthless ways, seeing the world as having turned its back on him just as Jiraiya did. He might form alliances with darker characters in the Naruto universe, believing they are the only ones who understand his pain.
Naruto's character would become more cynical. He'd lose his usual optimism and be more distrustful of others. His sense of justice might be warped, as he now feels that he has been wronged. He could start to see power as the only thing that matters, rather than the bonds he once cherished.
Naruto may also develop a darker side to his personality. The abandonment could make him feel betrayed and angry. He might struggle with controlling his emotions, especially his anger. However, this could also lead to him learning how to channel that anger into power in a more controlled manner, like he did with the Nine - Tails' chakra, but in a more refined way.
One possible plotline could be Naruto feeling extremely lost and having to find his own way to become stronger without their guidance. He might start to question his own worth and abilities, but then he could meet new allies who help him realize his true potential on his own. For example, he could encounter some other outcast ninja who have their own unique skills and together they form a new kind of ninja team that challenges the traditional ways of the ninja world.
Jiraiya might comfort Naruto by sharing his own experiences. He could tell Naruto about the times he faced difficulties and how he overcame them. For example, he might talk about his training with the toads and how he grew stronger through perseverance.
One possible reason could be that Naruto feels he has learned all he can from Jiraiya at that point. Maybe he has reached a level in his training where he believes he needs new experiences and challenges that Jiraiya can no longer provide.
In fanfiction, Jiraiya seeing Naruto as Hokage can be a very emotional moment. It could be a vision Jiraiya has in a story where he's still alive, or perhaps it's a memory in a story set after his death. This often shows Jiraiya's pride in Naruto and his belief in Naruto's potential to lead the village.
Their relationship would be very strong. Jiraiya would see Naruto as not just a student, but also as a connection to Minato. He would be strict but also very affectionate. Naruto would look up to Jiraiya as a father figure, since he never really had one. They would share many adventures together, with Jiraiya teaching Naruto about life, love, and ninjutsu.
One possible reason could be that in this fanfiction, Jiraiya might be preoccupied with other important matters. Maybe he has a secret mission that demands his full attention and he simply doesn't have the time to train Naruto. Another reason could be that there is some sort of conflict or misunderstanding between them that prevents Jiraiya from taking Naruto under his wing. For example, Naruto might have unknowingly offended Jiraiya in some way, or there could be a prophecy or external force that is keeping them apart for the time being.
In the Naruto universe, bringing someone back from the dead is extremely difficult. While there are some jutsu like the Edo Tensei that can reanimate the dead, it has its limitations and is often considered dark magic. For Naruto to revive Jiraiya, he would need to find a way around the natural laws of life and death. However, in fanfiction, anything is possible as it allows for creative interpretations and bending of the established rules.