I think that a lot of people are missing something important here. (Kari-no-sugata is the exception.)
Shallan's murder of her father (however it happened) shocked her deeply. It was a deep source of guilt for her, and was made much worse by the fact that it lead almost immediately into the crisis her family faced afterward. Because of this, she avoided thinking about it and almost never referred to the event. However, it informs everything she does in the book.
For one thing, I expect it was a huge part of why she wanted to leave home. Her plan with the soulcaster is reckless, yes. But anything is better than staying where *it* happened. This is also probably part of why she wanted to stay away at the end, despite her claimed loyalty to her family.
Another example, this one extremely important, is this: When Jasnyn kills those four footpads, it catalyzes Shallan's actual theft. I feel this is because Shallan feels so deeply that murder is wrong---and her own murder actually makes her hate it more. Seeing it happen, given her mixed-up feeling toward her own father, who may well have deserved to die, makes her reckless and she goes through with the theft. Thus the murder is sitting in the background behind a huge turning-point in Shallan's character arc. And we don't even see it until after the fact. This conclusion is supported even more by Shallan's study of philosophy---she concludes that Jasnah's act in killing the men was wrong. How does that then relate to her own actions? What does this tell about her?
With this insight, I feel that the reason she never brings up the Shardblade is because it is so intimately tied up with the guilt that she can't think straight about it. She only uses it in extreme situations. In my mind, despite it's inherent value, she just can't face what it means. Her not using it to help her family is an emotional response, not a logical one. And it's an important part of her character.
This is also why I feel that the dead man she draws must be her father. She ignores the situation with her father so studiously, I would be stunned if that wasn't what she was drawing. Her underplayed response to it actually makes me feel like that is exactly what it is---deep guilt, coming out and then being hushed up again dang quick. Something as simple as seeing somebody else's death would not have been ignored or left unexplained, I think.
With all of this, I cannot see the Shardblade having come from anybody but her father, after his death. I can't see Shallan as having killed anybody else, or see her referring to it as the fruit of her most heinous act for any other reason. The situations where this would have happened are really easy to imagine; at least one plausible one has been suggested here. There is no reason to think Shallan and her father would not have been completely alone when it happened (it's actually quite likely) and no reason Shallan could not have taken the blade in the second after his death, out of sheer stunned shock. How she would have gotten a Shardblade before the murder---I have no idea. If it involves her killing people, it's out. If it involves somebody giving it to her, you have to ask why it's the fruit, not the cause, or her most heinous act. It just doesn't make sense. I haven't seen a coherent theory that makes sense besides the one I've outlined here!