It's highly unlikely that the characters in 'House of the Dragon' would actually watch fanfiction about themselves. Fanfiction exists in our world, created by fans for fans, and the characters in the show are fictional entities within their own fictional universe. They don't have access to the fan - created stories about them.
You can try Archive of Our Own (AO3). It has a large collection of fanfiction, including many related to Daenerys and her dragons. Just use the search function and type in relevant keywords like 'Daenerys', 'dragon', and 'lemon' to find what you're looking for.
One popular one might be 'The Dragon's Queen Ascent' which delves into Daenerys' relationship with her dragons in a unique way. It shows how she uses their power in new and unexpected scenarios.
Yes, there are quite a few. You can start by checking out fanfiction websites like Archive of Our Own. There you might find some interesting stories that explore the concept of Daenerys and Jon in relation to the dragon form. Just search for relevant tags and keywords.
One common theme is power. Since they are associated with the dragon form, stories often explore how they use their new - found or enhanced power. Another theme is love. The relationship between Daenerys and Jon can be deepened or changed by their connection to the dragons.
Definitely not a true story. House of the Dragon is a work of imagination and creativity. It weaves a complex tale of power, politics, and dragons within a fictional realm.
Well, a simple idea could be that the pregnancy is a secret at first. Only a few close allies know. Jon and Daenerys have to be very careful to keep it that way. They might have some close calls where the secret almost gets out, adding a lot of tension to the story.