In many Sherlock fan fictions, Sherlock branding John could be a sign of his trust or a way to get a reaction out of him. It all depends on the author's imagination and the context they create.
In many Sherlock/John fanfictions, Sherlock's actions towards John show deep affection. For example, he often goes out of his way to protect John from danger. He might put himself in harm's way just to keep John safe, which can be seen as a sign of love. Also, his jealousy when John pays attention to others can be an indication. In some fanfictions, Sherlock is overly possessive of John's time and attention, much like a person in love would be.
Often, these fanfictions focus on the slow - burn aspect. Since Sherlock and John's relationship in the original series is platonic - ish at first, the fanfics gradually build up to the kiss. They also tend to explore the characters' emotions more deeply, like Sherlock's struggle to understand his own feelings.
If Sherlock was John's kid, it could change the nature of their relationship. There might be more protectiveness from John and a sense of inheritance in Sherlock's detective skills.
If Sherlock was John's kid, it would likely bring a unique emotional depth to the story. It might force them to confront personal issues while still trying to crack cases. It could be a fresh and exciting take on the usual detective duo.
A theme that often appears is the protection they have for each other. In fanfictions, you'll see Sherlock going to great lengths to protect John, and vice versa. It shows the strength of their bond. Also, the theme of self - discovery is common. Both John and Sherlock learn more about themselves as they navigate their relationship in these stories.
Well, in a lot of 'Sherlock and John married fanfiction', the theme of love and commitment is very prominent. It's about how they stay dedicated to each other through thick and thin. There's also the theme of growth. Both characters grow as individuals within the relationship. For example, Sherlock might become more empathetic, and John might become more patient. And the theme of their unique bond is always there. They have a relationship that's different from a typical married couple because of their detective work and their personalities.
Maybe John was frustrated at Sherlock's eccentric behavior. Sherlock often acts in ways that are outside of normal social norms, like his extreme focus on cases and disregard for basic social niceties. This could have led John to lash out and call him a 'freak' in a moment of exasperation.
Love and domesticity are common themes. It often shows how Sherlock, who is usually so focused on his work, now has to balance his relationship with John. For example, in many fanfictions, they have to figure out how to share household chores.