I'm not sure specifically as there could be many different interpretations. It might be a fan - created story where a character named Castle believes that Kate is cheating in the context of their relationship within the fan - created scenario.
The 'castle believes kate is cheating fanfic' could revolve around a breakdown in trust between Castle and Kate. It might start with Castle noticing some unusual behavior from Kate. For example, she might be spending a lot of time with another person. However, it could be that Kate is involved in a work - related project that requires her to be with this person often. But Castle, due to his insecurities or past experiences, starts to believe that she is cheating. The fanfic could then explore how they deal with this false accusation, whether they communicate effectively to clear up the misunderstanding or if it leads to a more serious rift in their relationship.
Obviously, Castle and Kate are the main characters. Castle is the one who has the belief that Kate is cheating.
I'm not sure specifically as there could be many different fanfics with that title. It might be about a character named Castle who has a strong belief that Kate is alive. Maybe Kate was in some sort of dangerous situation or presumed dead, and Castle is determined to prove she's alive.
The main characters are likely Castle and Kate. Castle is the one who believes Kate is alive, so he's a central figure in this fanfic. Kate, whether she's present or just the subject of Castle's belief, is also a main character as the story revolves around her being alive.
One common theme could be Castle's journey of grief. He might struggle to come to terms with her death, which could involve him isolating himself from friends and family. Another theme could be his determination to find out the truth behind her death, suspecting foul play even if others think it was an accident.
He becomes more withdrawn. Normally Castle is quite social and outgoing, but with Kate gone, he loses his spark. He may stop joking around as much and become more serious.
In a 'castle rescues kate fanfic', Castle may start his rescue mission when he discovers Kate has been kidnapped. He first tracks down the location by using his detective skills. Along the way, he might face some dangerous situations but his determination to save Kate keeps him going. When he finds Kate, she is weak but Castle's presence gives her new strength.
In a fanfic scenario where Beckett thinks Castle is cheating, she might initially be in denial. But as evidence mounts, she could become angry and start to distance herself from him. This is because trust is a huge part of their relationship, and if she thinks he's violated that trust, it would be a big blow to their connection. Maybe she'd also start to question all the other aspects of their relationship, wondering if things were ever real between them or if she misread him all along.
One possible plot is that Kate is in danger during an undercover operation. Castle, using his connections, gets wind of it and races to the scene. He manages to get her out just in time.
Yes, it might be a plot point in some fanfic. Fanfic often takes existing characters and creates various scenarios, so it's quite possible that in a particular Castle - related fanfic, Castle could witness Vaughn kissing Kate.
Some fanfic writers may have their own personal blogs or websites where they post their Castle fanfics. A Google search using relevant keywords such as 'Castle Kate Beckett pregnant fanfic blog' might lead you to these individual sites. However, be cautious as not all sites may be reliable or have high - quality content.