When she said she worked for "Nelson and Murdock" and I thought, "YEAH, YOU DO."
And yeah, the Daredevil/Murdock thing- I totally thought Frank knew, too. And maybe what Frank meant was that Murdock was a better person in general (he knows, for instance, that Daredevil or "Red" doesn't kill people- Frank talked a lot about being a monster with Karen.) Daredevil and Frank had long discussions about the justice/who deserves to die in Daredevil Season 2. It's another reason I think Frank might know- a way Matt disguises himself is that he doesn't really do that much talking with people in the suit, and when he does, he's in the shadows. If he, as Daredevil, hung out with Foggy in the suit, Foggy would've figured it out. Frank and Daredevil spent hours together, debating, and Frank listened to Matt Murdock in court. In addition to the ultimate fight with no mask in season 2.
I also just love how Bernthal plays this character- he does a bunch of little things, like "Does that Matt Murdock know you're here?" instead of "Does Matt Murdock know you're here?".
And I know Karen isn't everyone's favourite, but I love her in this. I wish there was more of her.