The project manager can use the burn up chart to analyze the current status of the project based on its scope (value delivered), budget (cost), and schedule (time). A burn up chart is a graphical tool that shows how much work has been completed (burned up) versus how much work remains (scope) over time. It also shows how much budget has been spent (burned up) versus how much budget remains (budget) over time. A burn up chart can help to monitor and control the project progress and performance and identify any variances or deviations from the plan. The chart given shows that both scope and budget lines are above their respective target lines at any given time point. This means that less work has been completed than planned (scope variance) and more money has been spent than planned (budget variance) at any given time point. Therefore, the project is behind schedule and over budget.

The project manager should use synchronous communication methods if they prefer to have immediate contact with team members. Synchronous communication is a type of communication that occurs in real time and allows for faster response times and more interactive discussions. Examples of synchronous communication methods include phone calls, video conferences, instant messaging, and face-to-face meetings. Synchronous communication can help to build rapport, clarify doubts, and resolve issues quickly among team members.
Synchronous communication should be used when the project manager prefers to have immediate contact with team members. Synchronous communication allows for real-time interaction and feedback, enabling faster response times and more interactive discussions. Reference: CompTIA Project+ Study Guide Section 3.1.3

The product owner is the person who is responsible for managing the product backlog, which includes adding, removing, or changing items based on stakeholder feedback and business value. The product owner is also the one who can collaborate with the development team and the scrum master to decide if a change can be accommodated in the current sprint or deferred to a future sprint. Therefore, the stakeholder should have asked the product owner to request the change instead of the team member, who is not authorized to make changes to the sprint backlog12.

This answer is based on the best practice of choosing a project management methodology that suits the project characteristics and environment12. Scrum is an agile framework that is designed to handle complex and uncertain projects with frequent changes and tight deadlines34. Scrum involves a small, cross-functional team that works in short iterations called sprints, delivering incremental and potentially shippable products at the end of each sprint5. Scrum also allows for continuous feedback and improvement through daily stand-up meetings, sprint reviews, and retrospectives6. Scrum is suitable for this project because it can accommodate the high uncertainty, the risk of requirement changes, and the tight deadlines, while also enabling the two developers to collaborate effectively and deliver value to the customer. Reference = CompTIA Project+ Certification Study Guide7, CompTIA Project+ Certification Exam Objectives8, Project Management Methodologies Comparison (11 PM Methods)6, Project Management Methodologies: 12 Best Frameworks [2023]7, What is Scrum?5, Scrum Methodology: The Ultimate Guide6

A milestone chart is a tool that shows the key events or deliverables of a project along a timeline12. A milestone chart is useful for tracking the progress of a project that has technical tasks and requires a SME's knowledge, because it can provide a high-level overview of the project status, without getting into the details of each task or activity34. A milestone chart can help the PM and the project lead communicate the project achievements, challenges, and expectations to the stakeholders, and also identify any potential risks or delays that may affect the project completion56. A milestone chart is better than the other options because:
A Gantt chart is a tool that shows the tasks, dependencies, durations, and resources of a project along a timeline7. A Gantt chart is more detailed and complex than a milestone chart, and may not be suitable for providing high-level updates to the stakeholders8.
A project organization chart is a tool that shows the roles, responsibilities, and reporting relationships of the project team members and other stakeholders9. A project organization chart is not a tool for tracking project data, but rather for defining the project structure and authority10.
A Program Evaluation Review Technique (PERT) chart is a tool that shows the tasks, dependencies, and critical path of a project along a network diagram. A PERT chart is more focused on the sequence and timing of the project tasks, and may not capture the key milestones or deliverables of the project.
Reference = CompTIA Project+ Certification Study Guide, CompTIA Project+ Certification Exam Objectives, What is a Milestone Chart?1, How to Create a Milestone Chart in Excel in 3 Steps2, Milestone Chart: The Easiest Way to Track Project Milestones3, How to Use Milestones in Project Management4, What is a Gantt Chart?5, Gantt Chart vs Milestone Chart: What's the Difference?6, What is a Project Organization Chart?7, How to Create a Project Organization Chart8, What is a PERT Chart?9, PERT Chart vs Gantt Chart: What's the Difference?10