Yes, there are many. Some might focus on their adventures together in the Naruto world, exploring their unique dynamics. For example, a fanfiction could be about them teaming up on a mission and gradually realizing their feelings for each other during the process.
One common theme is the exploration of their unspoken feelings. Since they are both part of the Naruto universe, there could be a lot of tension between them that fanfictions like to play with.
One common plot is that Karin uses her unique abilities as a sensor - type ninja to get closer to Suigetsu in a seductive way. For example, she might sense his emotions and use that knowledge to her advantage. Another plot could be that they are on a mission together, and Karin decides to try and seduce Suigetsu to make the mission more interesting or to gain some sort of upper hand. Sometimes, it might also involve a love triangle situation where Sasuke is somehow involved, and Karin's seduction of Suigetsu is a way to make Sasuke jealous.
In the Naruto universe, Karin seducing Suigetsu is more likely to be just a fanfiction concept. Their personalities are quite different. Karin is often very focused on Sasuke, and Suigetsu has his own goals and a rather brash personality. While in fanfiction, authors can create all kinds of scenarios for them to interact in a seductive way, it doesn't seem very likely within the main storyline's character dynamics.
One possible plot could be that they accidentally get pregnant and then have to deal with the reactions of their friends and the ninja world. There could be a lot of drama as they try to figure out how to handle the situation while also facing their own personal feelings for each other.
Naruto, having been banished, may initially lose his sense of purpose. However, with Karin by his side, he could find a new reason to strive. He might develop a more nuanced view of the ninja world and its politics. Karin, on the other hand, could develop a softer side. She has always been in a tough situation, but Naruto's kindness could make her more empathetic. She may also start to trust others more, especially Naruto, which is a big step for her character.
I'm not sure if there are many popular ones specifically about that. However, you could try searching on fanfiction platforms like FanFiction.net or Archive of Our Own. Maybe look for Naruto - related fanfiction (since Suigetsu and Karin are from Naruto) and then filter through the stories to find ones that might touch on this idea.
I'm not sure specifically about 'lemon' fanfics (which often imply adult content), but there are many great fanfics about Suigetsu and Karin that focus on their relationship development in a more general way. You can try searching on fanfic platforms like FanFiction.net or Archive of Our Own and filter for stories tagged with their names.
Well, 'Suigetsu x Reader' fanfiction often explores a unique relationship. In such stories, the writer can really play with the dynamic between Suigetsu's character traits, like his edginess perhaps, and the reader - insert character. It can be an exciting way to experience the world of the story from a more personal perspective, as if you are right there in the story with Suigetsu.
Well, it depends on what you consider 'good'. There are numerous 'naruto x karin romance fanfiction' works. However, the quality varies. Some may focus more on the emotional connection between them, while others might be more action - oriented with the romance as a side plot. You really have to dig in and read a few to find the ones that suit your taste.