Well, initially, Naruto might show kindness towards the Nine - Tails despite it being a powerful and somewhat feared entity. He could try to communicate with it on a deeper level. The Nine - Tails, in turn, might be intrigued by Naruto's tenacity. As time passes, they begin to trust each other more. Naruto may share his dreams and fears with the Nine - Tails, and the Nine - Tails might start to see Naruto as someone worthy of its friendship.
Sometimes, other characters from the Naruto universe might also play important roles in these fanfictions. For example, Kakashi could be involved as Naruto's mentor, giving advice on how to better communicate with the Nine - Tails. Or Sakura might be there to support Naruto in his journey of befriending the Nine - Tails, even if she doesn't directly interact with the tailed beast.
A really cool plot might be that Naruto and the Nine - Tails enter a spiritual realm together, where they have to complete a series of challenges to strengthen their bond. These challenges could test their trust, courage, and ability to work as a team. Along the way, they meet other spirits that either help or hinder them in their quest.
Naruto's relationship with his friends undergoes significant changes. His closest friends like Kakashi would be on high alert. Kakashi would constantly be watching Naruto to make sure he doesn't lose control. With his peers, some might start to distance themselves, fearing the unpredictable nature of the Nine Tails' power. However, true friends like Rock Lee would see it as an opportunity for Naruto to grow stronger. Lee might encourage Naruto to master the Nine Tails' power and use it for good. Naruto's relationship with his friends becomes a complex web of trust, fear, and support as he deals with the Nine Tails' possession.
Maybe through new jutsu or abilities. The fanfiction could give Naruto some unique power that allows him to communicate or negotiate with the Nine - Tails on a different level. He could use this power to show the Nine - Tails a different perspective, like the potential for harmony between them instead of constant struggle.
One key moment could be when Naruto is in a tough battle and the Nine - Tails willingly lends him extra power without hesitation. It shows that the Nine - Tails trusts Naruto enough to let him use its strength.
Sonic would probably be very confused at first. He might mistake Tails in Amy's body for the real Amy and be really surprised by her different behavior. Knuckles would likely be suspicious and keep asking questions. Cream might be worried about her friends and try to help them figure out what happened. Big the Cat probably wouldn't notice much difference at all, just going about his normal fishing routine.
Yes, in some fanfictions, Naruto is often depicted as having a very special connection to the Nine - Tails that goes beyond the normal relationship in the original story. For example, he might be able to fully control the Nine - Tails' power in ways not shown in the canon, or they could have a mental bond that allows for unique forms of communication and cooperation.
Another unique exploration could be through a shared goal that is not related to the main Naruto plot. For example, they both want to protect a special place in the spirit world that has significance for the Nine - Tails. To do this, they have to work together in a way that they haven't before. Naruto has to use his human skills and the Nine - Tails has to use its tailed - beast powers in harmony. This would show a different side of their relationship, one based on mutual respect for each other's abilities.
To develop the baby nine - tails, it could be given a unique personality trait such as being very empathetic. So, it can not only feel Naruto's emotions but also those of other villagers. This causes it to try and bridge the gap between Naruto and the villagers who fear it. It might go out of its way to show the villagers that it means no harm, which in turn would make for an interesting character arc as it tries to change the perception of the nine - tails in the village.