In the comics, the Punisher isn't simply heartless. His actions are a result of his traumatic past and a determination to fight crime by any means necessary. It's a mix of passion and a warped sense of morality.
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.
To the best of my knowledge, Eminem has no presence in Marvel Comics. Marvel Comics typically focus on superheroes and their adventures, and Eminem's profile doesn't align with that universe.
It's possible for Rachel to be in the Punisher comics. However, her presence might be limited to certain storylines or special editions. Not every iteration of the comics includes her.
The Punisher comics have had a variety of writers. One such writer is Chuck Dixon, whose work on the series left a significant mark. Different authors have shaped the Punisher's adventures in their unique ways.