The Project Plan in PRINCE2 identifies the management stages and timescales of a project. This plan provides an overview of how and when the project's objectives are to be achieved, by showing the major products, activities and resources required for the project, and structuring them within a timescale.
References: PRINCE2 Foundation manual, PRINCE2 official resources

In PRINCE2, an 'internal' dependency refers to a relationship between two products of a project that is under the control of the project team. These dependencies are managed within the project's boundaries, unlike external dependencies which involve elements outside the project's direct control.
PRINCE2 7 Foundation materials on product dependencies.

The purpose of the 'Directing a Project' process in PRINCE2 is to enable the project board to be accountable for the project's success by making key decisions and exercising overall control while delegating the day-to- day management of the project to the project manager. This includes the authority to initiate and close the project, deliver stage boundaries, and be updated on project progress.
= PRINCE2 7 Foundation handbook and online resources

Project Assurance in PRINCE2 is focused on the project's adherence to standards and procedures within the project environment, providing a project-level view of compliance. In contrast, Quality Assurance is an organizational level function that oversees compliance across all projects and operations, ensuring that the entire organization follows the prescribed standards. References: PRINCE2 Foundation Training Manual; PRINCE2 2017 Foundation handbook.

The Controlling a Stage process is used by the Project Manager to maintain focus on the delivery of the stage's products within the agreed tolerances. This involves assigning work, monitoring such work, managing issues and risks, and ensuring that the stage remains on track in terms of time, cost, quality, scope, risk, and benefit performance. References: PRINCE2 Foundation official documentation and study materials.