The objectives of the 'managing a stage boundary' process include confirming to the project board that there are no products outstanding for the stage (1) and requesting the project board to approve work to start on the next stage (4). These objectives ensure that each stage is properly concluded before moving to the next, maintaining project governance and alignment with planned objectives.
PRINCE2 7 Foundation materials on the 'managing a stage boundary' process.

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

According to the 'manage by exception' principle in PRINCE2, when any forecast indicates that tolerances are likely to be exceeded, this issue must be escalated to the project board for decision-making. This principle supports efficient use of management time by only involving them when necessary, such as when predefined thresholds are anticipated to be breached.
PRINCE2 7 Foundation handbook and documentation on the 'manage by exception' principle.

This statement is correct as it highlights the individual differences among team members who may have similar skills and experiences but approach tasks differently. This variability can influence the way tasks are executed within a project, impacting team dynamics, project management approaches, and ultimately the project's success. Recognizing and managing these differences are crucial for effective team collaboration and project delivery.
(PRINCE2 7 Foundation Handbook, AXELOS)

The change budget in a PRINCE2 project is designed to fund changes that involve an increase in the agreed scope of the project. Such changes typically require additional budget allocations as they extend or modify what the project initially planned to deliver. References: PRINCE2 Foundation official study guide and online resources.