If the 13-year-old commits murder, are the parents liable? Are the parents liable for any of the kid's law-breaking actions?
How's downloading illegal music any different?
...when their child commits murder? There are plenty of cases in the US and the UK available to research. Unless you hand your kid the gun, or don't leave YOUR gun lying around (applies to the US mostly), only the child ends up in (a special, depending on age) court. Then of course, in the US there are plenty examples where a 12 year old is tried as an adult, but that still leaves out the parents.
As for your second question, of course! If they are directly responsible. You cannot send your child to commit a crime thinking YOU won't be punished.
Your 3rd question, you DO know that even in the US civil and criminal law are two very different things?
So, to sum it up, are you just trolling because you immediately dislike something you hear, and are too lazy to invoke some more modern parts of your brain instead of just the knee-jerk reaction part?