Regarding your first question, I remember learning a Beis HaLevi that may have dealt with that topic. It was at least 15 years ago, so I can’t remember if it answered your question or not, but I’m pretty sure that it dealt with the topic.
Regarding your third question (the one in parenthesis), I think the answer is connected to the discussion on the Chilul Hashem thread and the source you brought there from the Mesilas Yesharim (thank you).
If you shoot an arrow at someone in order to kill him, and in fact, he does die, he only died because Hashem wanted him to die. Essentially, Hashem killed him, and not you. You are being punished for the fact that you used your bechira to choose to shoot an arrow that you knew could end up killing someone.
But actually, I don’t understand your question altogether. Even without my answer, and even if you want to say that you are being punished for the effect of your actions and not the bechira involved, what difference would it make if it’s the same arrow or not? Either way, it was your original action that led to its being there, so who cares if it’s the same arrow?