Does everyone in the Muslim religion believe that all non-believers should be killed?

No that is ludicrous and stupid. Very few uneducated Muslims may believe this because of western forces keep invading Muslim countries and keep killing Muslim men, women and children. In last 10 years US forces have killed over one million Muslims in Iraq and Afghanistan and still end doesn't seems near. If such circumstances make some Muslims become extremists, you can't blame them to think that way.