In situations where unforeseen problems prevent the planned execution of a project, the project manager should focus on problem-solving and collaboration to keep the project on track. According to the PMBOK Guide, the project manager's responsibilities include engaging with stakeholders to meet project requirements and creating customer satisfaction1. The Professional in Business Analysis Reference Materials also emphasize the importance of collaboration and stakeholder engagement to address issues and find solutions2.
Therefore, helping the customer find an alternative location aligns with the project manager's role in facilitating project success and maintaining stakeholder satisfaction. References:
* PMBOKGuide - Seventh Edition, Project Management Institute1.
* Professional in Business Analysis Reference Materials, PMI2.

A project manager who has team members around the world in different time zones should plan and schedule the tasks and work packages in a way that minimizes the dependency and communication gaps between the offices. This can be done by using techniques such as rolling wave planning, agile methods, or critical chain method, which allow for more flexibility and adaptability in the project schedule. The project manager should also consider the cultural differences, working hours, holidays, and availability of the team members when planning and scheduling the project work. This way, the project manager can avoid delays, conflicts, and misunderstandings caused by the geographical and time zone challenges. References:
A Guide to the Project Management Body of Knowledge (PMBOK Guide) - Seventh Edition, Chapter 3:
Project Performance Domain, Section 3.2: Schedule Performance, pp. 55-56 Project Management Professional (PMP) Handbook, Section 2.2: PMP Exam Content Outline, Domain II:
Process, Task 2: Plan and manage project schedule, pp. 15-16
Managing Projects Across Time Zones, by ProjectManager.com, published on July 9, 2019

In an agile environment, integration is not a separate phase that happens at the end of the project, but rather a continuous activity that happens throughout the project. Integration involves combining the work of different teams or individuals into a coherent whole that meets the customer needs and expectations. Frequent and continuous integration of work allows the project team to obtain early feedback, identify and resolve issues, and learn from the results. This helps to improve the quality, performance, and value of the product, and to reduce the risk of rework, delays, and defects. Therefore, the project manager should have ensured frequent and continuous integration of work to avoid the integration issues and the decline in the product release progress. The other options are not as effective or appropriate as frequent and continuous integration. Forming a separate quality assurance team to test all items at the end of each sprint would create silos, delays, and dependencies, and would not foster collaboration and ownership among the teams. Performing a Scrum of Scrums on a regular basis to help the teams remove impediments would be a good practice, but it would not address the integration issues directly, and it would depend on the frequency and quality of the communication and coordination among the teams. Arranging an online session on the integration concept and suggesting tools to the teams would be helpful, but it would not ensure that the teams actually integrate their work frequently and continuously, and it would not provide feedback and learning opportunities. References: Agile Practice Guide, 1st edition, Chapter 3.4.2, 3.5.2, PMBOK Guide, 6th edition, Chapter 4.4.2, 4.6.2

When faced with a potential delay due to a vendor's resource shortage, the project manager should engage the project team to explore alternative options to adhere to the schedule. This aligns with the principles of project management, which emphasize proactive problem-solving and collaboration to maintain project momentum. The PMBOK Guide highlights the importance of communication and stakeholder engagement in managing project risks, including those associated with vendor deliverables. By discussing alternative options, the project manager can facilitate a solution-oriented approach that may involve re-allocating resources, adjusting work priorities, or finding other ways to mitigate the delay without compromising the project's objectives or quality standards.
PMBOK Guide and the Project Management Institute's (PMI) resources on project risk management and stakeholder engagement12.