The purpose of the Risk theme in PRINCE2 is to establish a cost-effective procedure to identify, assess, and control the uncertainties or risks that can affect the achievement of project objectives. This involves understanding how risks can impact the project and managing them proactively to ensure project success.
References: PRINCE2 Foundation Training Manual; PRINCE2 2017 Foundation handbook.

The authorization to deliver the project's products is given during the Directing a Project process. This process involves the Project Board's decision-making responsibilities, including granting permission to proceed with the project after the initiation phase and authorizing the delivery of stages as the project progresses. References: PRINCE2 Foundation manual, PRINCE2 official resources

In PRINCE2, if the role of project support is not allocated to another person, it is assigned to the project manager. Project support involves assisting with the management of the project by handling administrative tasks, configuration management, and other support functions. References: PRINCE2 Foundation Handbook, Project Support section.

Section: Volume B
Explanation/Reference: http://prince2.wiki/Managing_Product_Delivery#Objective