One possible antagonist could be a villain from their past who sees the pregnancy as a vulnerability. For example, a meta - human they previously defeated might come back to target them, thinking that with Caitlin pregnant, they'll be distracted and easier to take down.
Yes, there are quite a few. You can start by looking on popular fanfic websites like Archive of Our Own. Just search for 'Barry Allen and Caitlin Snow married' and you'll likely find a variety of stories with different takes on their relationship, from fluffy domestic scenarios to more action - packed adventures where they are a married couple fighting crime together.
There might be. It depends on the writer's intention. If they want to create a story that can be read by all ages, they would avoid any inappropriate content. For example, they could write about the baby being a symbol of hope in their superhero - filled world, and how Barry and Caitlin's journey towards parenthood makes them better people. They could also include cute moments like shopping for baby things together.
Another storyline could be that they planned the pregnancy. They've been in a stable relationship for a while and decided it was time to start a family. The fanfic could then focus on their preparations for the baby, like decorating the nursery and going to parenting classes. Along the way, they might also have to deal with any threats from their enemies who see the pregnancy as a way to get to them.
Often, such a fanfic would involve their relationship development as a married couple. It may start with their wedding day, showing all the emotions and the reactions of their friends like Cisco and Iris. Then it could move on to how they combine their lives, perhaps they move into a new house together. There might be parts where they argue over small things, like Barry leaving his Flash suit all over the place, which shows a more realistic side of their relationship. And of course, there would be moments of great love and affection, like surprise date nights or just cuddling on the couch after a long day.
You can try fanfiction websites such as Archive of Our Own (AO3). It has a large collection of fanfics on various topics, including ones related to Barry Allen and Caitlin Snow. Just use the search function and type in the relevant keywords like 'Barry Allen', 'Caitlin Snow' and 'pregnant' to narrow down your search.
A plot could revolve around Caitlin and Barry being forced to work undercover as a couple to infiltrate a criminal organization. As they pretend to be in love, they start to realize their true feelings for each other. Or perhaps Caitlin's scientific knowledge and Barry's speed are the only things that can stop a city - wide disaster caused by a malfunctioning S.T.A.R. Labs experiment.
Definitely not. It involves inappropriate and private sexual matters that violate social ethics and good taste. There are so many other positive things to talk about like hobbies, achievements, and cultural experiences.