Yes. This has been known to happen when people are bullied to the point that they see no escape and begin having difficulty thinking about the consequences of their actions. If you are being bullied it is vital that you talk to someone you trust about what you are experiencing.
Yes. Unfortunately yes, it happens. It often is one of the main social ingredients, if you will, in school shootings we hear about in the news so often. People get hurt and killed, and without effective and enforced anti-bullying policies in place, nothing gets solved.