Why did Historia see her father's memories?
As far as I know, it was never discussed as of the release of the most recent chapter. That specific scene in Chapter 68 was mostly what happened in the anime. It could be explained in a future chapter. 
Looking closely at Episode 9, 


   it can be seen that after the flashbacks of her father's memories, Historia opens her eyes as if surprised at what she saw. This might mean that her eyes were closed during the flashback scenes, implying that she saw her father's memories.


In the manga, this was not exactly what happened. 


  She just widens her eyes and opens her mouth slightly as he killed him and as her father's memories were shown. From my interpretation, it could be that she was just surprised at what she had done.