Fem Naruto's relationship with Jiraiya would be interesting. Jiraiya, being a perceptive person, would try to help her find her voice in more ways than one. He might teach her to write down her thoughts and feelings. This would bring them closer as she would trust him with her innermost secrets. Also, her relationships with the villagers would change. Some might pity her at first, but as they see her determination and strength, they would come to respect her more.
Her relationship with Sasuke could be really different. Since she can't express herself verbally, Sasuke might initially misunderstand her. But as he gets to know her better, he realizes that her actions speak louder. For example, when she saves him from danger, he starts to see her in a new light. With Sakura, they might develop a more sisterly bond as Sakura tries to help Fem Naruto communicate in different ways.
Her relationship with Sasuke could be interesting. Sasuke might initially be dismissive of her because of her disabilities, but then come to respect her tenacity. For example, when they train together, she might surprise him with her ability to adapt. With Sakura, they could bond over the fact that they are both different in their own ways. Sakura might learn some of her sign language to communicate better.
Her relationship with Hermes could be really interesting. Since Hermes is the messenger god, he could be the one to help her understand the complex world of the Greek gods. They might start as just acquaintances, but as she needs to send messages or get information quickly, they become closer friends. With Athena, there could be a bit of a rivalry at first because Fem Harry is intelligent and so is Athena. But over time, they could learn from each other and respect each other's wisdom.
With Harry and Ron, they would become more protective of her. They'd have to learn to read her body language more carefully. For example, when she used to shout out answers in class, now she'd have to communicate her thoughts through gestures, and they'd have to be more attentive. And with Snape, he might initially think she was being disrespectful by not answering verbally, but then come to understand her situation and respect her even more for her determination to continue learning despite her handicap.
At first, Shikamaru might be a bit indifferent to the mute character, but as Naruto shows his kindness and determination to include the mute person, Shikamaru would start to get involved. They would gradually form a bond as they discover each other's strengths. Naruto's strength and Shikamaru's wisdom would complement each other, and they would both learn to communicate with the mute character in different ways, thus deepening their relationships.
In terms of their relationship with their families, if they have any remaining family members. Naruto's family, like Jiraiya (if he's still alive in this fanfiction) could be overjoyed and offer all kinds of support. Sasuke's family, perhaps Itachi (again, if alive) might have a more complex reaction, being both proud and worried about the future of the Uchiha bloodline with this new development.
Her relationship with the camp counselors would be really complex. They have to protect the camp and its inhabitants, so they'd be hesitant to fully trust her. However, as she participates in camp activities and battles, she could earn their respect. In terms of romantic relationships, a son of Athena might be initially attracted to her intelligence but then struggle with her heritage. And she might have a mentor - like relationship with an older demigod who has also had a difficult family history.
The relationships could develop gradually. At first, Naruto might be a bit wary of the Fem Kyuubi and Fem Bijuu because they are so different from what he's used to. But as they fight together against common enemies, a sense of trust could start to form. For example, if they save each other's lives in battle, that would strengthen their bond.
With the villagers of Konoha, Naruto was once seen as a hero. But his leaving could cause mixed feelings. Some might see it as a betrayal, while others might respect his choice. Fem Sasuke was always an enigma in Konoha. Her leaving might be seen as expected by some, but for those who hoped she would fully integrate into the village, it would be disappointing. And as they journey outside Konoha, they will meet new characters, and their relationships with them will be based on their new identities as outcasts from Konoha.
The female Kyuubi might start with a relationship of distrust towards Naruto. After all, the Kyuubi has a long history of being feared and hunted. But as Naruto shows her kindness and understanding, she could gradually warm up to him. The female Juubi, being a more mysterious and powerful being, might be initially indifferent to Naruto. However, when she sees his determination and the good in him, she starts to respect him. Their relationships would develop through shared battles and experiences, with Naruto constantly proving himself to be a worthy ally and friend.
The relationships could develop in a very complex way. Fem Amaterasu might initially be aloof because of her divine nature. However, Naruto's tenacity and his own special powers would draw her in. Fem Kyuubi, having a more primal connection to Naruto already, would further strengthen that bond. As they go on adventures together, Naruto would often be the mediator between Fem Amaterasu and Fem Kyuubi. Their different personalities would clash at times, but through Naruto's influence, they would learn to work together and eventually form a strong and loving relationship with Naruto at the center.