The project charter is a key document that outlines the scope, objectives, and stakeholders of a project. If team members are asking questions about the training that the project will provide, the project manager should first review the project charter to determine if this training is within the project's scope. If it is not, the project manager should submit a change request to include this training in the project scope. This ensures that all project activities are aligned with the project's objectives and that any changes to the project scope are properly managed. References: A Guide to the Project Management Body of Knowledge (PMBOK Guide) from www.pmi.org. Specifically, the section on Project Scope Management, which discusses the importance of managing project scope and handling change requests.

When a project experiences a delay that could impact the schedule, the project manager should capture the risk in the risk register. This allows for the documentation of the risk and its potential impact, as well as the planning of appropriate response actions to mitigate the risk. The risk register is a key tool for risk management in projects, as it provides a structured way to track and monitor risks throughout the project lifecycle. By capturing the risk, the project manager can work on preventing the risk from becoming an issue, which aligns with the proactive approach to risk management advocated by PMI.
(Project Management Institute. (2021). A Guide to the Project Management Body of Knowledge (PMBOK Guide) - Seventh Edition and Standards. Project Management Institute.)

According to the PMBOK Guide, 6th edition, section 8.3.3.1, the project manager is responsible for monitoring and controlling the project quality and ensuring that the project deliverables meet the quality requirements. The project manager should also document any quality issues or defects that are identified during the quality control process and take appropriate actions to correct them. In this scenario, the project manager should first update the issue log, identify the involved stakeholders, and assign resources to the corrective actions. This will help to track and resolve the quality issue and prevent further deviations or rework. The other options are either premature or irrelevant, as they do not address the root cause of the problem or respect the authority and scope of the project manager. References: PMBOK Guide, 6th edition, section 8.3.3.1, page 287.

When a team member is experiencing personal issues that affect their work, it is important for the project manager to show empathy and provide support. Understanding the team member's situation can help in finding ways to assist them, whether it's through offering flexible work arrangements, providing access to counseling services, or temporarily reallocating tasks. This approach not only helps the team member but also maintains the cohesion and productivity of the team.
The PMBOK Guide highlights the importance of project managers supporting team performance, which includes recognizing and addressing personal issues that may impact work1. Additionally, the Professional in Business Analysis (PMI-PBA) materials emphasize the role of the project manager in understanding and supporting team members to ensure that personal issues do not hinder project progress234.

* According to the PMBOK Guide, 6th edition, section 9.4.2.3, the project manager should use conflict management techniques to resolve conflicts among team members and stakeholders.3
* Some of the conflict management techniques are: problem solving, compromising, smoothing, forcing, and withdrawing.3
* In this scenario, the project manager has tried problem solving (holding a meeting to work out a permanent solution) and compromising (asking them to find a way to resolve the issues), but these techniques were unsuccessful.4
* The project manager should not use smoothing (emphasizing areas of agreement and avoiding areas of disagreement), forcing (imposing a solution), or withdrawing (avoiding or postponing the conflict), as these techniques may not address the root cause of the conflict or may worsen the situation.4
* Therefore, the project manager should escalate the issue to a higher authority, such as the functional manager, the sponsor, or the steering committee, who have more power and influence in a weak matrix environment.4
* Escalating the issue to a higher authority may help to resolve the conflict, protect the project objectives, and maintain the team performance and morale.4 The references for this answer are:
1: PMP Exam Questions | 100% Free PMP Example Questions 2: PMP Practice Exam 1 | Free PMP Exam Questions 3: PMBOK Guide, 6th edition, Project Management Institute, 2017, pp. 349-350. 4: [Conflict Management Techniques for the PMP Exam - PM Study Circle] : [PMP Exam Prep: Project Human Resource Management - Simplilearn]