Identify whether or not a crime has been committed in each of these cases. In each case, discuss fully why this is, or is not, a crime.

1. Ken, a 6 year old boy, was pretending to be a cowboy while playing with his father's pistol. He loaded the pistol as he had seen his father do in the past. He then took the pistol and shot his brother.
2. Jeremy, while in the boys' washroom at school, set fire to a roll of hand towel. As a consequence of his actions serious fire and smoke damage occurred in the school.
3. One evening while coming home from a friend's home, Joyce was stopped by a police officer for driving her moped without lights and reflectors.
4. One evening while home alone, Heather heard a noise downstairs in her kitchen. Nervous, she grabbed her husband's revolver from the bedside table. While terribly frightened, she made her way down the darkened stairs. Seeing a shadow, she fired the gun in its general direction. Unknowingly, she killed her husband who returned home two days earlier than expected from a business trip out of town.
5. While walking across someone's lawn, a post officer fell down a large hole that had been dug because of a blocked sewage pipe. The hole was uncovered, and not indicated by a warning sign. The post officer had always walked the same route while delivering mail to his customer for years

Please answer this.