According to the Project Management Professional (PMP) Reference Materials, the project manager should submit a change request to accelerate the project as requested by the customer when the key subcontractor asked for additional budget. This is because a change request is a formal proposal to modify any document, deliverable, or baseline of the project1. In this case, the change request would affect the project schedule, cost, and scope baselines, as well as the contract terms with the subcontractor. Therefore, the project manager should follow the change control process to document, analyze, approve, and implement the change request2.
The other options, A, B, and C, are not the first actions that the project manager should take. Asking upper management for more funds and updating the project budget may not be feasible or necessary without a proper justification and approval of the change request. Revising the project scope to cope with the budget changes may not satisfy the customer's needs or expectations, and may also require a change request. Updating the risk register and project log, and managing the budget closely are important activities, but they are not sufficient to address the change request and its implications. References: 1: A Guide to the Project Management Body of Knowledge (PMBOK Guide) - Sixth Edition, Chapter 4.6.1, "Change Requests". 2: A Guide to the Project Management Body of Knowledge (PMBOK Guide) - Sixth Edition, Chapter 4.6.3, "Perform Integrated Change Control".

According to the Project Management Professional (PMP) principles, when there is a discrepancy between the received sample and the expected specifications, the project manager should first refer to the procurement contract. This contract would contain the agreed-upon specifications and would serve as the reference point for any disputes. By doing this, the project manager can ensure that the supplier's claim about the measurement being accurate is indeed correct, or if the project engineer's complaint about the sample not being the correct length is valid. References: PMBOK Guide - Sixth Edition, Section 12.3.3.1: Control Procurements

The project manager's role includes managing day-to-day operations and ensuring the project is completed on time, on budget, and achieves its objectives1. When unexpected changes occur, such as the need for team members to work remotely and incur operational expenditures, it's important to follow the Perform Integrated Change Control process. This process involves reviewing all requested changes, approving changes, and managing changes to deliverables, organizational process assets, project documents, and the project management plan2. In this case, the project manager should submit a change request to address the additional costs incurred by the team members. This ensures that the project's budget and schedule are updated accordingly and that the project continues to align with its objectives.
References:
Project team roles and responsibilities1
Assembling a Project Team: Roles, Responsibilities & Best Practices2

In an agile project, it's crucial to ensure that all requirements, including compliance standards, are met. The project manager should meet with the compliance team to understand their requirements and ensure they are included in the Definition of Done (DoD) for each story. The DoD is a clear and concise list of requirements that a software increment must meet to be considered complete. By including the compliance requirements in the DoD, the project manager can ensure that each increment of the project meets the organization's compliance standards, thereby mitigating the risk of non-compliance. References: Project Management Professional (PMP) Reference Materials, Professional in Business Analysis Reference Materials.