Nazism is far-right and authoritarian. Socialism is just far-left, but not necessarily authoritarian. Soviet-style socialism was very authoritarian and that's why it got its bad reputation. And you can be authoritarian and not even be on the left-right axis - Saudi Arabia is an example, as is Afghanistan now.
Maybe, but they don't have really free markets either. In this regard, North Korea is more of an absolutist monarchy than any previously known form of socialism.
