Regression testing is crucial to ensure that new changes do not negatively impact existing functionalities. The IS auditor should recommend that regression testing be conducted to confirm that the system operates correctly after changes are made.
References
* ISACA CISA Review Manual 27th Edition, Page 256-257 (Testing Strategies)

The advantage of using agile software development methodology over the waterfall methodology is that it allows for quicker deliverables. Agile software development is an iterative and incremental approach that emphasizes customer feedback, collaboration, and adaptation. Agile software development delivers working software in short cycles, called sprints, that typically last from two to four weeks. This enables the development team to respond to changing requirements, deliver value faster, and improve quality. Waterfall software development is a linear and sequential approach that follows a predefined set of phases, such as planning, analysis, design, implementation, testing, and maintenance. Waterfall software development requires a clear and stable definition of the project scope, deliverables, and expectations before starting the development process. Waterfall software development can be slow, rigid, and costly, especially if changes occur during the later stages of the project. References: CISA Review Manual (Digital Version), Chapter 3:
Information Systems Acquisition, Development & Implementation, Section 3.1: Project Management Practices

The organization is primarily responsible for the security configurations of the deployed application's operating system when migrating its HR application to an Infrastructure as a Service (IaaS) model in a private cloud. This is because in an IaaS model, the cloud provider is responsible for the security of the underlying infrastructure that they lease to their customers, such as servers, storage, and networks, while the customer is responsible for the security of the areas of the cloud infrastructure over which they have control, such as operating systems, middleware, and applications. Therefore, the organization needs to ensure that the operating system is properly configured, patched, hardened, and monitored to protect the HR application from unauthorized access or malicious attacks.
The other options are not primarily responsible for the security configurations of the deployed application's operating system. The cloud provider's external auditor is not responsible for any security configurations, but rather for verifying and reporting on the cloud provider's compliance with relevant standards and regulations.
The cloud provider is responsible for the security of the underlying infrastructure, but not for the operating system or any software installed on it by the customer. The operating system vendor is responsible for providing updates and patches for the operating system, but not for configuring or securing it according to the customer's needs.
References:
* 11: What Is IaaS (Infrastructure As A Service)? - Forbes
* 12: What is Shared Responsibility Model? - Check Point Software
* 13: Who Is Responsible for Cloud Security? - Security Intelligence

The primary factor to determine system criticality within an organization is the maximum allowable downtime (MAD). MAD is the maximum time frame during which recovery must become effective before an outage compromises the ability of an organization to achieve its business objectives and/or survival. MAD reflects the business impact of a system outage on the organization's operations, reputation, compliance, and finances. MAD can help to prioritize system recovery efforts, allocate resources, and establish recovery objectives.