Hamlet confronts his mother in scene 4, and she responds with expressions of guilt. Does she seem to realize that Claudius murdered Hamlet's father?

From the text, she has no idea about the murder. She didn't realize that Claudius murdered Hamlet's father.

Explanation:

When Hamlet confronted his mother Gertrude, the guilt she expressed was for marrying Claudius inappropriately. But, she did not seem to know of the role Claudius played in the murder of Hamlet's father, when Hamlet presses her on it, her response is, "Alas, he's mad."

Therefore from the text, Gertrude had no idea what Hamlet was referring to when he talked about the murder of a king. She didn't realize that Claudius murdered Hamlet's father