One possible fanfiction could be about Neji and Sakura going on a mission together. In this story, they might start off as just comrades but gradually develop a deeper understanding of each other. Neji's calm and composed nature could contrast with Sakura's more fiery and determined personality, leading to some interesting interactions.
In fanfiction, one way to develop their relationships is through a series of challenges. Let's say they are all put in a survival situation. Neji's calm and calculating nature would help them plan. Sakura's medical skills would keep them alive. Naruto's determination would keep their spirits up. During this time, they would learn more about each other's fears and hopes. Naruto might realize that Neji has a soft side, and Neji would see Naruto's growth. Sakura would become closer to both of them as they rely on each other. This would strengthen their relationships in different ways, like a bond forged in the fires of adversity.
A third plot could revolve around a mission where Naruto, Sakura, and Neji are the only ones available. They are sent to a mysterious land filled with strange creatures and a powerful enemy. Neji uses his Byakugan to analyze the enemy's weak points. Sakura heals them during the battles. Naruto, of course, is the one who ultimately faces the main villain, with the support of his friends.
In fanfiction, Neji and Sakura could form an unlikely alliance against a common foe within the Hidden Leaf Village. This could be due to some political intrigue where they have to trust each other despite their different personalities.
In some Neji and Sakura fanfictions, they might be part of a new team. This team could be facing a powerful new enemy. Neji's calm and strategic thinking combined with Sakura's determination and healing abilities would make for an interesting dynamic. The fanfiction could detail their training together to face this enemy, and how they develop their skills and teamwork.
Rock Lee might be an interesting choice. He is Neji's friend and has a strong sense of loyalty. He would be very dedicated to taking care of the baby. His physical strength could also be useful in case of any danger. And his positive attitude would be great for the baby's environment.
Well, a fanfiction could start with Sakura being in danger during a battle. Neji, being protective and possessive, goes to extreme lengths to save her. He uses his Byakugan to its fullest extent, not caring about his own safety. After the battle, Sakura realizes how much Neji values her and his possessive nature is actually a sign of his deep care for her.
Another possibility is that they are rivals in a friendly way. They could constantly compete to see who can improve faster in different aspects such as medical ninjutsu (for Sakura) and Byakugan - related skills (for Neji). This rivalry could push them both to reach new heights in their respective skills and at the same time, deepen their respect for each other.
There is. Try searching on Archive of Our Own (AO3). It has a large collection of fanfictions. The sakura and neji love fanfictions there often delve deep into their characters. Maybe one has them working together on a mission and slowly realizing their feelings for each other, or perhaps a story where they have to pretend to be in love for a mission and then it becomes real.
There is some. For example, in some fanfictions, they might be paired up during a mission where they have to rely on each other deeply. This shared experience could be the start of a romantic connection. However, not all fanfictions in this regard are of high quality, so you need to read reviews or summaries first.