One common theme is the struggle between Daryl's wild, survival - instinct side and his new role as a married man. He has to balance protecting his family and still being true to his own nature. Another theme is the building of a family in a post - apocalyptic world. This includes not just having children but also creating a sense of community within the family unit.
There is a fanfiction called 'Married to Daryl Dixon: A Different World'. It portrays an alternate universe where Daryl is married and has to deal with both the normal relationship issues as well as the threats from the outside world. It's interesting to see how the author weaves the character's personality into a married life scenario. There are also some stories on fanfiction.net that you can search for using the keywords 'Daryl Dixon married' to find more options.
Appropriateness varies. If the abuse fanfiction is part of a story that ultimately aims to heal or show growth, it might be okay. But if it makes light of abuse or uses it in a way that makes viewers or readers uncomfortable without any redeeming qualities, it's not appropriate. Writers should be aware of the impact their work can have on the fan community.
Daryl Dixon isn't gay in the comics. The storylines mainly revolve around his adventures and struggles in a post-apocalyptic world, not his sexual orientation.