When a project manager returns from an absence to find a nearly complete project schedule developed by the team, the priority should be to ensure that the schedule aligns with the project's vision and objectives. This is crucial because the project scope statement, which includes the project's vision, objectives, and work breakdown structure, guides all project activities. The project manager must review the developed schedule against the approved project scope statement to ensure that all project work aligns with the documented objectives and deliverables. If discrepancies are found, the project manager should work with the team to make necessary adjustments. This approach helps maintain the project's integrity and ensures that the final deliverables will meet the stakeholders' expectations.
(Based on the Project Management Professional (PMP) guidelines and standards from PMI's resources123

The project manager should foster an environment where open discussions are encouraged, as they can lead to more comprehensive understanding and better decision-making. However, it is also important to adhere to the ground rules to ensure that discussions are efficient and considerate of everyone's time. This approach is in line with the PMBOK Guide's principles of stakeholder engagement and team management, which emphasize the importance of balancing open communication with meeting management1. It also aligns with the PMI Professional in Business Analysis (PMI-PBA) standards, which advocate for effective stakeholder engagement and collaboration2.
References:
PMBOK Guide - Seventh Edition1
PMI Professional in Business Analysis (PMI-PBA) reference materials2

A project manager should mentor the team member who is asking for directions and actions on many tasks, as this indicates a lack of confidence, competence, or clarity in the team member's role and responsibilities.
Mentoring is the process of providing personal support and guidance to a less experienced team member by a seasoned project manager. A mentor can help the team member develop their skills, knowledge, and abilities, as well as provide feedback, advice, and encouragement. A mentor can also help the team member understand the project objectives, scope, deliverables, processes, and standards, and how to align their work with them.
By mentoring the team member on a regular basis, the project manager can help the team member improve their performance, productivity, and quality of work, as well as increase their motivation, engagement, and satisfaction. References: Project Management Professional (PMP) Certification | PMI, Mentoring - Key Competency for Program and Project Professionals, What Good is a Project Manager Mentor? | PMI

To gain the support of an influential stakeholder who is skeptical about the value of project management processes, the project manager should clarify the project roles and responsibilities and share the purpose of the project management processes. This approach helps in aligning the stakeholder's understanding with the project objectives and demonstrates how the processes add value to the project's success. Engaging the stakeholder in this manner is more likely to result in their buy-in and support, as it addresses their concerns directly and shows a willingness to collaborate and communicate effectively12345.
: The approach of clarifying roles and sharing the purpose is supported by PMI's guidelines on stakeholder engagement and is consistent with best practices in project management and business analysis12345678.