The purpose of the plans theme in PRINCE2 is to facilitate the management and control of the project by establishing whether the project's targets are achievable. This involves setting out how and when the project's objectives are to be achieved by defining the necessary resources, activities, timescales, and costs. References:
PRINCE2 Foundation Handbook, Plans Theme section.

Applying the 'focus on products' principle in PRINCE2 helps to ensure stakeholder expectations are met by providing a common understanding of the project's products. This principle emphasizes the importance of clearly defining what the project has to deliver, in terms of both scope and quality, so that there is no ambiguity about the expected deliverables, thereby aligning expectations and project outputs.References: = PRINCE2 7 Foundation handbook and online resources

The risk response type "Exploit" is specifically designed to ensure that the opportunity is realized. This response is proactive and aims at making changes to exploit the opportunity fully, which aligns with managing opportunities within PRINCE2 risk management. References: PRINCE2Foundation Training Manual; PRINCE22017 Foundation handbook.

In the context of PRINCE2, the integrated elements include the principles, themes, processes, and tailoring PRINCE2 to the project environment. 'The products' are not listed as one of these integrated elements.
Instead, they are outputs or deliverables that result from applying the PRINCE2 methodology to project management. References: PRINCE2 Foundation manual, PRINCE2 official resources

In PRINCE2, the collective name for individuals or groups who may be affected by or can influence a project is "Stakeholders." This includes a wide range of people such as customers, users, team members, and suppliers, each of whom has an interest in the project's successful execution and outcomes. References:
PRINCE2 Foundation manual, PRINCE2 official resources