Explanation
The risk manager should increase stakeholder risk appetite by explaining risk handling and mitigation strategies, which will help stakeholders understand how risks can be managed and reduced, making them more comfortable with the risk process.
The best way to increase stakeholder risk appetite is to explain risk handling and mitigation strategies, which are the actions taken to reduce the probability and/or impact of risks, or to enhance the opportunities. By doing so, the risk manager can help the stakeholders understand how the risks can be managed effectively and efficiently, and how the potential benefits can outweigh the potential costs. This can also increase the stakeholder confidence and trust in the risk process and the project outcomes. The other options are not appropriate ways to increase stakeholder risk appetite. Excluding risk averse stakeholders from future risk discussions can alienate them and create conflicts. Increasing the impact of all risks in the risk breakdown structure (RBS) can exaggerate the risk exposure and create unnecessary fear and anxiety. Developing a generous probabilistic cash flow model can create unrealistic expectations and lead to poor decision making.
References: PMI Risk Management Professional (PMI-RMP) Examination Content Outline and Specifications, page 81. A Guide to the Project Management Body of Knowledge (PMBOK Guide) - Sixth Edition, pages 403-4042.

The risk manager should recommend that the project manager review the plans for the key activity, as this will help identify potential issues and opportunities to improve the activity's performance and reduce its impact on the critical path.
The risk manager should recommend the project manager to review the plans for the key activity, which is now on the critical path according to the Monte Carlo simulation. The critical path is the sequence of activities that determines the minimum possible duration of the project. Any delay on the critical path will affect the project completion date. Therefore, it is important to review the plans for the key activity and identify any potential risks, issues, or opportunities that may affect its performance. The risk manager and the project manager should also evaluate the feasibility and effectiveness of any risk response strategies for the key activity, such as fast-tracking, crashing, or resource optimization. The other options are not appropriate recommendations for the risk manager to make. Adding more float to the key activity is not possible, since the critical path has zero float by definition. Adding more contingency to the project may not address the specific risks or issues related to the key activity. Increasing the budget for the key activitymay not improve its duration or quality, and may also increase the project cost baseline unnecessarily. References: PMI Risk Management Professional (PMI-RMP) Examination Content Outline and Specifications, page 91. A Guide to the Project Management Body of Knowledge (PMBOK® Guide) - Sixth Edition, pages 215-2162. Project Critical Path Analysis Using Monte Carlo Simulation3.

Categorizing risks by their impact on project objectives ensures that risk response plans are aligned with project priorities. This helps in focusing on the most critical risks and their potential impact on the project's success.
Categorizing risks by their impact to the project objectives is a way of aligning the risk management process with the project goals and stakeholder expectations. By doing so, the risk management professional can ensure that the risk response plans are focused on the most critical aspects of the project and that the project priorities are being considered in the decision making. This approach can also help to communicate the value of risk management to the project team and the stakeholders, as they can see how the risk management activities are contributing to the project success. Categorizing risks by their impact to the project objectives does not necessarily help to identify the specific causes of risks, determine the level of project leadership and organizational involvement, or assign risks and risk severities to functional disciplines and departments. These are other possible ways of categorizing risks, but they are not the main purpose of using the impact to the project objectives approach. Reference: PMI-RMP Certification Handbook1, page 9; PMBOKGuide, page 415.