The purpose of a Risk Register in PRINCE2 is to capture all the risks that may impact the project throughout its duration. It serves as a tool to document the details of each identified risk, including their nature, potential impact, and proposed responses. This register is continuously updated as new risks are identified and as existing risks evolve or are resolved.References: PRINCE2 7 Foundation handbook and official documents.

The 'learn from experience' principle in PRINCE2 is applied to ensure that lessons are sought, recorded, and acted upon throughout the life of the project. This principle helps the project team to replicate successes and avoid repeating past mistakes, thereby improving the efficiency and effectiveness of the project.
References: PRINCE2 Foundation Handbook, Learn from Experience section.

In PRINCE2, the responsibility for documenting any tailoring of the Business Case theme, along with other themes, generally falls to the Project Manager. This includes documenting how the theme is being applied in a particular project context, ensuring the approach remains appropriate and meets the project's requirements.References: PRINCE2 Foundation Manual

Risk tolerance is defined as the measurable threshold that represents the tolerable range of outcomes for each objective at risk. It quantifies the level of exposure to risk that an organization or project can withstand, helping to guide risk response planning and risk management strategies.References: (PRINCE2 7 Foundation Handbook, AXELOS)

Within the context of a PRINCE2 quality review meeting, the role of Chair is recommended and crucial.
The Chair's responsibility is to ensure that the review meeting is conducted methodically and remains focused on its objectives. This includes leading the discussion, ensuring that all issues are aired and discussed properly, and that the meeting runs within its allocated time. This role is distinct from that of the Project Manager, Assurance, and Producer.References: PRINCE2 7 Foundation study guide and official documents.