A minimum requirement for applying the Plans theme in PRINCE2 is that team managers in the project must prepare team plans. This ensures that each part of the project controlled by a team manager is adequately planned in line with the overall project plan and stage plans. These team plans provide detailed guidance on how products will be delivered within the constraints set by the project management.References:
PRINCE2 7 Foundation resources and study materials.

The objectives of the 'Closing a Project' process in PRINCE2 include ensuring that provisions are made for ongoing benefit realization reviews (objective 1) and handing over any ongoing issues, including unresolved risks or threats, to operational maintenance or support teams (objective 4). This process is about wrapping up the project cleanly, ensuring that all project objectives related to closure are met, and preparing for the sustained realization of benefits post-project.References: = PRINCE2 7 Foundation Training Manual and official PRINCE2 website documentation

Product-based planning in PRINCE2 focuses on defining and understanding the project's outputs or products.
This method helps in determining the project's approach by clarifying what products must be delivered, thus guiding the planning of activities and resources needed to create these products. It ensures that the project's structure and execution strategy are aligned with delivering tangible, well-defined outcomes.References:
PRINCE2 7 Foundation resources on product-based planning.

The Quality Management Approach in PRINCE2 should provide guidance on how and when prototyping is to be used within the project. This approach outlines the quality techniques and standards to be applied and the responsibilities for achieving the required quality levels. Prototyping, as a method to validate product quality and user requirements early in the development cycle, falls under these guidelines.References:
(PRINCE2 7 Foundation Handbook, AXELOS)

When defining risk tolerance, the factors considered include the Project Board's attitude towards risk, the organization's risk appetite, and the level of risk deemed acceptable by the Project Board. The allocated risk budget is not a direct consideration in defining risk tolerance; rather, it is a resource aspect managed within the tolerances set for the project. References: PRINCE2 Foundation Training Manual; PRINCE2 2017 Foundation handbook.