The Frankfurt School were German left leaning academics trying to come to terms with how the promise of modernity led not to socialism but the holocaust and the gulag. That really is it.
No, that really isn't it. Marcuse for example remained optimistic about the utopian possibilities of revolution, and he was the greatest intellectual influence on the New Left.
I'm not sure what your first sentence means. The CIA's contact with the F-School is well-documented, so I assume you're not disputing that?