Happyman, you're entirely too hung up on the meanings of those two words. Although I agree that her father is the most likely former owner of Shallan's shardblade, it's still possible that it had another source. I don't there's anything wrong with her calling it the "proceeds" of an act or "fruit" of her sin if she took it from her father and killed him with it, or killed him with it while stopping him from claiming it for himself for some reason. But since you're pretty set in your viewpoint, why don't you go with this one: the shardblade fell out of the air after he died and cut through his coat. He doesn't even have to be wearing the coat in that scenario, just needs it nearby.
I guess how likely this is depends on how Shardblades respond to being held by someone who is not their owner. Is it even possible to steal a shardblade? If you grab it, do you claim it, or what? These are good questions.
Call me pedantic, though, but I still feel that the words I cited are strong evidence in favor of the simplest scenario of Shallan killing her father through mundane means and then getting the blade. This simple cause-effect relationship is well-established in-world and is one that Shallan would know about. It agrees with the simplest interpretation of the image she made of her father. Everything else requires introducing new rules or speculating well beyond the evidence or weakening the simple statement I cited as evidence (and yes, your proposed alternate interpretations are not impossible, just weaker, because they don't match the usual meaning of the words). I just considered that quote the best evidence (it's really close to being the
only evidence of what actually happened) and wanted it accounted for.
As for the fabrial---we don't know what happened to it. And that's the rub-we don't know! It's an empty spot. But emptiness isn't evidence, just room for more speculation.
As for whether killing her father would be considered a terrible sin---well, a few points to consider:
(1) She calls herself a murderer when referring to her father's death. No rationalizations behind that word. The Spren accepts it, too.
(2) She reacts badly to the death of four people who were ready to rape and kill her, and whom she had never met.
(3) She feels tremendous guilt over her families situation and her place in it.