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.
It's hard to say for sure. 'Karen' could be a blend of real incidents and creative imagination. Sometimes, such stories take real-life inspirations but are embellished for entertainment value.
I don't think there was a character named Karen in Punisher comics. Usually, the main characters and well-known ones are pretty distinct, and I haven't come across a Karen in this series.
In 'Karen Eiffel Stranger than Fiction', Karen Eiffel is a key character. She is a writer, and her actions and the story she is writing are central to the plot. Her role creates a unique situation where the fictional world she is creating intersects with the real life of the other main character in a very strange and unexpected way.