Do you think a purely Capitalist Society would be a free one? Why or why not?
There are various degrees of capitalism. One side of the spectrum is complete hands-off approach, on the other, some government intervention. And "free", of course, is an abstract idea.
So you see, it's kind of hard to answer your question.
I know that many socialist societies couldn't care one bit for capitalist freedoms. Not because a big boss sits at the head of the government and hits people on the head with utopian propaganda, but because people really do like communal living. To them introducing capitalism would tear their social fabric apart. To them, introducing capitalism would be taking away their freedom.
I don't know. You can write books about this question. It's not a simple answer. And, I truly believe that people who have never lived in socialist societies can't understand them well enough to be able to answer questions like these. I'm not talking about totalitarian regimes who are locked in battle against The Empire, spending resources on weapons instead of social services. I'm talking about a non-aggressive, non-expansionist society, not in any war with any country or group or ideology, just living peacefully on its own. I.e., not North Korea, and not the Soviet Union. I don't know enough about China, and it's in a state of change as we speak, so it's hard to comment on them.
I know that the state of Israel was founded on socialist principles, way before 1948, and that despite the well-known obstacles it was facing (wars, masses of immigrants with no adequate infrastructure to handle them, a British occupation, blockades, etc.) the social fabric there was pretty healthy, even when times were hard economically. An agricultural / manufacturing economy is also a good one. Having a tertiary economic sector is not a requirement ... i.e. services like financial services, "consulting", etc.
Socialism can be a beautiful thing. Gentle socialism, of course. Not utter central control.