One common theme is Matt's internal struggle with his pain. Since he's hurt, it often explores how he copes with his physical and emotional pain while still being Daredevil. Another theme is his relationships, like his friendship with Foggy or his romantic interests. How they react to his hurt state and support him is often a big part of the stories.
You can start by looking on fanfiction platforms like Archive of Our Own (AO3). It has a large collection of Daredevil fanfics. Just search for 'Daredevil Matt Hurt' and you'll get a list of relevant stories. Another option is FanFiction.net, though the tagging system there might require a bit more digging to find exactly what you're looking for.
Sure, it can be normal. Just like any person might be interested in what others write about them or their alter - ego. It's a way to connect with the fan community on a different level.
Well, it could be a way for the daredevil to see how others perceive their character. Maybe they find it interesting to see the different scenarios and relationships that fans come up with in the fanfiction.
We don't have enough information to know exactly who Karen is. She could be an ordinary person, a student, a teacher, or just someone who likes to read stories.
Given only 'dateline karen read story', Karen's identity remains a mystery. She might be a staff member at Dateline who was reading a story for work purposes. Or she could be a person who was interviewed by Dateline and was reading a story during the interview, or she could be an ordinary person whose story - reading experience is being highlighted in relation to Dateline.
Matt could be a new superhero in the fanfic. Maybe he has some unique powers or abilities that haven't been seen before. He might be a street - level hero who has a different perspective compared to the Avengers.