What tasks do you think Configuration Manager should perform (or performs) in your team?
Managing the build and release process, working with both the dev team and ops teams in their middle ground.
What is primary responsibility of Configuration Manager?
Constantly removing any manual processes from both build and release, to limit risk during production release.
What are secondary/auxiliary responsibilities of Configuration Manager?
Improving the relationship and inherent mistrust issues between the dev and ops teams.
Does Configuration Manager need to be in charge of development processes on the project/company or he should be told what to do?
Like any role, the better the CM is, the less he needs to be managed. But he should be servicing both the dev and ops teams' needs and resolving conflict from those needs, as opposed to making up problems that don't exist and "solving" them.
What are relations between Configuration Manager, Build Manager, Release Manager, CI Manager roles? Aren't they all the same - Configuration Management?
I would say that Configuration Management is comprised of all the others. You may have a CM team where different people have different roles. Or you may have one CM who does it all.
Maybe term Configuration Management is redundant and Technical/Team Lead should do all the related work instead?
No. The team lead should be managing the people and the technical lead should be managing the application. If you trust in CM to be done by either of these roles, it will simply never get done (except in very small companies ... maybe).