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.)

During iteration planning, it is crucial to identify and manage dependencies between teams to ensure smooth project progression. When a deliverable from one team is dependent on another team's output, the project manager should inform the dependent team of this relationship and collaborate to plan the deliverable accordingly. This proactive communication helps in aligning the teams' efforts and schedules, thus avoiding delays and ensuring that the deliverables are completed as per the project timeline.
: = Iteration planning practices emphasize the importance of identifying and accounting for dependencies between teams1. The PMBOK Guide also highlights the need for effective communication and coordination among project teams to manage dependencies2.

The project manager should evaluate the impacts of the changes that were made to the project without any approval. This is because any change in the scope can affect the other project constraints, such as time, cost, quality, risk, and stakeholder satisfaction. The project manager should use the change management plan and the integrated change control process to assess the impacts of the changes, determine the appropriate actions, and obtain the necessary approvals. The project manager should also communicate with the project team member who made the changes and explain the importance of following the change control procedures. The project manager should not remove the changes without evaluating them, as they may have some value or benefit for the project. The project manager should not add team members to the project without analyzing the resource requirements and availability. The project manager should not update the project documentation with the new scope without validating and approving the changes. References: (Professional in Business Analysis Reference Materials source and documents) PMBOK Guide, 6th edition, Section 4.6, pp. 129-131 PMI Professional in Business Analysis (PMI-PBA) Examination Content Outline, Domain IV: Traceability and Monitoring, Task 3, p. 13 Business Analysis for Practitioners: A Practice Guide, Section 5.4.2, p. 118

Following the stakeholder engagement plan is the best option for the project manager in this situation. The stakeholder engagement plan is a document that describes how the project manager will communicate with, manage the expectations of, and involve the stakeholders in the project decisions. By following this plan, the project manager can ensure that the decision about the new timeline is made in a transparent, collaborative, and timely manner, and that the stakeholders are informed and satisfied with the outcome. References:
(Professional in Business Analysis Reference Materials source and documents) PMBOK Guide, Seventh Edition, Section 13.2.3, "Stakeholder Engagement Plan" Professional in Business Analysis (PMI-PBA) Guide, Section 5.3.2, "Stakeholder Engagement"

In Agile project management, collaboration is key to resolving issues such as disagreements on feature scope.
The project manager should facilitate a collaborative environment where all team members can contribute to the discussion. This approach aligns with Agile principles, which emphasize teamwork, customer collaboration, and the ability to respond to change12. It's important for the project manager to encourage open communication and ensure that all voices are heard, which can lead to a shared understanding and agreement on the feature's scope34. This not only helps in resolving the current issue but also strengthens the team's ability to work together effectively in future sprints56.
: = Agile methodologies advocate for close collaboration among team members to effectively define and deliver features that meet business needs7. The Project Management Institute (PMI) also highlights the importance of negotiation and conflict resolution skills in Agile environments to address scope disagreements and ensure project success1. Additionally, the role of the Business Analyst in Agile projects involves facilitating collaboration between the Product Owner, Development Team, and Stakeholders to ensure alignment with business objectives7.