CCC isn't a hacker space as I understand the term. CCC is a club of security experts. hacker spaces are communal spaces where you can tinker with peers using provided tools.
That there is also a branch of very public security experts is... Incidental, I'd say.
No. It happens that a lot of members are security experts but it is far far broader than that.
The CCC is a very decentralized organization. A lot of hacker spaces are in fact operated by local subdivisions or are completely independent organizations but with a lot of overlap in membership.
In general the CCC likes define itself more by those who share its values and less by the legal entity with that name.