The project manager should first gather more information about the previous project's issues by interviewing the other project manager. This will help in understanding the root causes of the delay and how to prevent similar issues in the current project before taking further action.
The project manager should first include the risk of delay in delivery of the GTG in the risk register and communicate with the stakeholders about the potential impact and response strategies. This is part of the risk identification process, which is the first step in risk management. The risk register is a document that records the identified risks, their causes, effects, probabilities, impacts, and response plans. The project manager should communicate with the stakeholders to ensure that they are aware of the risk and its implications, and to obtain their feedback and support. The project manager should also update the risk register as new information becomes available or as the risk status changes. The other options are not the first actions that the project manager should take. Communicating with the client to provide the previous shutdown plan is part of the risk response process, which comes after the risk identification and analysis processes. Reviewing and updating the project schedule is part of the schedule management process, which is not directly related to risk management. Interviewing the other project manager to learn more details is a technique that can be used to identify risks, but it is not the first action that the project manager should take. The project manager should first document the risk in the risk register and communicate with the stakeholders before seeking more information from other sources. Reference: 3, 4, 5

The risk manager should perform a quantitative risk analysis to determine the potential impact of risks on the project's completion date. This will help in providing a more accurate project completion date to the customer, considering the risks and their potential effects on the project schedule.
According to the PMI Risk Management Professional (PMI-RMP)® Examination Content Outline1, one of the tasks in the domain of Risk Analysis is to perform quantitative risk analysis using techniques such as Monte Carlo simulation, decision tree analysis, sensitivity analysis, etc., to quantify the possible outcomes for the project and their probabilities, and to evaluatethe cost and schedule impacts of risks1. In this scenario, the risk manager should perform aquantitative risk analysis and update the results, because the project costs have increased significantly and the customer has imposed a strict deadline for the project completion. A quantitative risk analysis will help the risk manager to estimate the probability of meeting the project objectives, such as cost and schedule, and to determine the appropriate contingency reserves for the project. A quantitative risk analysis will also provide more accurate and reliable information for the customer and the project team, and will support the risk response planning process2. References: 1: PMI Risk Management Professional (PMI-RMP)® Examination Content Outline, page 92: A Guide to the Project Management Body of Knowledge (PMBOK® Guide) - Sixth Edition, pages 431-432.

An affinity diagram is a tool used to visually organize and group risks or ideas based on their similarities and categories. It helps in structuring the risks for further analysis and discussion. (Reference: PMBOK Guide, 6th Edition, p. 138) According to the PMBOK Guide, an affinity diagram is a tool and technique for the identify risks process that allows large numbers of ideas to be sorted into groups for review and analysis. An affinity diagram can help the risk manager to visually organize the risks identified in the pre-workshop survey by grouping them into categories based on their similarities or common characteristics. This can help the risk manager to facilitate the risk analysis and prioritization in the workshop, as well as to stimulate new patterns of thinking and generate additional risks.
Some of the other options are not relevant or appropriate for the question scenario:
The analytical hierarchy process is a technique for the plan risk management process that provides a method for comparing and ranking alternatives based on multiple criteria. It is not a tool for visually organizing risks.
A SWOT analysis is a technique for the identify risks process that examines the project from the perspective of its strengths, weaknesses, opportunities, and threats. It is not a tool for visually organizing risks, but rather for generating them.
Assigning probability and impact is a technique for the perform qualitative risk analysis process that assesses the likelihood and the potential effect of each individual risk on the project objectives. It is not a tool for visually organizing risks, but rather for evaluating them.