One common theme is the relationship development between Kate and Castle. Her pregnancy might bring them closer or create some new challenges in their relationship.
You can try searching on popular fanfiction websites such as Archive of Our Own (AO3) or FanFiction.net. Just type in 'Kate Beckett pregnant' in their search bars and browse through the results.
In this fanfiction, perhaps Kate initially hides her pregnancy from Jack because she's afraid of how he'll react. But as time goes on, she starts to show signs that are hard to conceal. Jack finally figures it out when he catches her having a bout of morning sickness. He is initially shocked but then becomes very protective. They then have to face the reactions of the other survivors, some of whom are supportive while others are worried about the added burden.
In this type of fanfiction, other characters on the island would surely have reactions. Some might be happy for them, while others could be jealous or worried about how a baby would change the group dynamics. Their pregnancy could also be a catalyst for the group to find a more stable living situation on the island.
In a Sea Patrol Kate - pregnant fanfiction, Kate could be pregnant with a child of one of her fellow crew members. This could create a whole lot of drama on the ship. There might be relationship issues to deal with, as well as concerns about the future of the child in the military - like - environment of the Sea Patrol. However, they all work together to make the best of the situation.
Yes, there are quite a few. You can start by looking on popular fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'Castle Beckett pregnant' in their search bars, and you'll be presented with a variety of stories. Some might focus on how Castle and Beckett handle the pregnancy, while others could explore the reactions of their friends and family.
The plot could be that Kate's pregnancy is a result of a moment of hope and love they shared on the island. Jack is determined to keep her and the baby safe. He uses his medical skills to monitor Kate's health closely. The other survivors see this as a sign of new life and hope for their community on the island. However, there are also those who are jealous or worried that the baby will draw unwanted attention from the island's mysteries.
The popularity might be due to the fans' love for the characters. Castle and Beckett have a great chemistry, and seeing them in a new situation like a pregnancy is exciting. It allows fans to imagine a different side of their relationship.