My first guess as to why that might be so is a difference in laws and law enforcement, but that is only a guess.
Could be. Of course our laws, in general, developed from English common law, but the divergence since then is likely substantial. I'm not very knowledgable on law enforcement differences to be honest.
Of course, in the US you can walk around anywhere outside of the major urban centers and see less violence and crime than Europe.
The US crime rate is driven almost purely by urban violence in high population centers. Outside of these areas, the crime rate is virtually non-existant.
Perhaps, but Europe is far more urban than the United States and that still doesn't explain the difference in Canada, who has a massive rural and urban population.
Also, a bit of commonsense plays a part here too. For criminal activity one needs opportunity. For opportunity one likely needs other people nearby. Hence, urban areas will simply offer more opportunity in a far smaller area.
It is still interesting, to me, that crime is more of a problem here than there (and you're right that violent crime is especially much higher).