2. (b) That's right. B has dealt with C only as A's representative. This means that, although B was physically present and involved in the process of making the contract, he was not personally involved in the legal consequences of these acts. Whatever he did, it was as if A himself were doing those things, and the legal consequences therefore accrue only to A and not to B.
It is generally the case that an agent does not acquire legal rights or obligations when acting on behalf of their principal. In the present case, it follows that B is not a party to the contract between A and C, and C cannot sue B on the contract.