Authors often show Sasuke's determination through his actions. He might travel long distances to find Sakura. For example, he could be going through dangerous terrains just to reach her. This physical journey represents his inner determination to get her back.
There is no appropriate fanfiction with such vulgar content. Fanfictions usually explore the characters' relationships in a more positive, respectful way, like Naruto's relationship with his comrades in Team 7 and how they overcome difficulties together.
In the realm of fanfiction, almost any scenario is possible. Regarding Sasuke divorcing Sakura for Karin, it may exist. Fanfiction authors draw inspiration from the source material and then take it in new directions. The idea might stem from Karin's past feelings for Sasuke and some fans' desire to see how such a relationship shift would impact the characters. It could also be a way to explore the characters' personalities more deeply, for example, how Sakura would cope with such a betrayal and how Karin would handle being with Sasuke in that context.
Yes, there are likely some fanfictions out there where Sasuke marries Karin. You can try searching on popular fanfiction websites like FanFiction.net or Archive of Our Own (AO3).
There probably is. Fanfiction writers like to take existing characters and create different storylines. But it's important to note that this isn't part of the official Naruto story. In the original, Sasuke and Sakura are a couple, and Karin has her own relationship with Sasuke which is more of comradeship in the official plot. Fanfiction just gives people the freedom to deviate from the original.
Sakura is also a key character. Her feelings and reactions to Sasuke's attempts are crucial. She may be conflicted, angry, or slowly start to soften towards him. And in a lemon fanfiction, her relationship with Sasuke will likely be explored in a more romantic and perhaps even sexual way, depending on the nature of the fanfiction.
Sasuke can prove it by being honest about his feelings. He could sit down with Sakura and tell her directly how he has felt all this time and that he made a mistake in leaving. For example, he might say, 'Sakura, I've realized that you are the most important person to me and I want to be with you again.'
Well, perhaps Sasuke has been on a journey of self - discovery and during that time he understood that Sakura was the one he always loved. He might come back to the village and start by simply being around Sakura in a non - intrusive way. He could help her with her medical work or protect her on her missions. Gradually, he'd open up about his feelings and hope that she still has feelings for him too.
There could be a fanfic where Naruto, Sakura, Sasuke, and Karin wake up with a hangover after a wild celebration in the Hidden Leaf Village. Maybe they had a party to celebrate a big victory against an enemy. Naruto would probably be the first to wake up, feeling groggy but still ready to face the day. Sakura, on the other hand, might be a bit grumpy and complain about the headache. Sasuke would be his usual stoic self, but even he couldn't hide the fact that he wasn't feeling his best. Karin would be using her medical skills to try and ease the pain for everyone. It could be a humorous fanfic with lots of banter between the characters as they deal with the after - effects of their drinking.