(b) That's only partly right. It is true to say that the directors of a company can exercise all the powers of the company (except for any matters that specifically require the authority of the members). Directors can employ people to work for the company; authorise individuals to represent the company as agents; borrow money; enter into contracts, eg for goods or services; leases, etc; or enter into agreements to acquire or sell property. When managing a company, directors must make decisions and act in accordance with their own best judgment. They are not subject to direction from the members in relation to day-to-day management decisions. If members don't like the management decisions of the directors, they can remove the directors, but otherwise the members cannot interfere in the decision-making of the directors.
However, the common law and the Corporations Act 2001 impose duties on directors which regulate how directors exercise their powers. In particular, directors are required to always act with reasonable care and in good faith.
Good faith means that directors must exercise their management powers with proper discretion, for proper purposes, and in the best interest of the company. They must avoid placing themselves in a situation where their own personal interests conflict with the interests of the company, because they have a duty to promote and safeguard the company's interests.
If one or more director acts in breach of these duties, the other directors may bring an action on behalf of the company on grounds of the breach, seeking appropriate relief.