(a) That's wrong. In general partnerships, every partner is entitled to take part in the management of the partnership business. The extent to which each partner actually does this may be limited by agreement.
Partners generally have the authority to act as agents of the firm, and to carry out legal transactions in the course of conducting the firm's business. This means that a partner can normally do all of the following things on behalf of the firm: make and receive payments; acquire and transfer property; enter into contracts; perform and discharge contracts; make representations; and provide and receive information.
The usual authority that partners have can of course be modified by agreement. The agency power of a particular partner might, for instance, be limited by agreement. But in such cases, the partner in question might still have an ostensible authority that will continue to bind the firm, unless and until the persons they might deal with are notified of the limits that have been agreed to. Such notice can be given individually to persons with whom the firm has already done business, and suitable advertisements in appropriate newspapers in regions where the firm does business will be sufficient notice to others of a partner's limited authority.