It would take 1 au / speed of sound in string. The 8 minutes comes from the (much faster) speed of light.
Based on some googling it seems it would take roughly 1.8 years.
Based on some googling it seems it would take roughly 1.8 years.
Same question.
If it doesn't follow any laws of physics, then there is no predictable relationship between any input and its action (since if there was such a predictable relationship, it would be a law of physics that the string was obeying.)