The consultant should ask about the success metrics for the project to understand the goals and expectations of the Career Services department and how to measure them. This will help the consultant design a solution that aligns with the department's vision and needs. Which users need system admin access and what is the estimated project budget are questions that can be asked later in the project planning or execution phase, not during the discovery session. Reference:
https://trailhead.salesforce.com/en/content/learn/modules/education-cloud-basics/education-cloud-discovery
https://trailhead.salesforce.com/en/content/learn/modules/education-cloud-basics/education-cloud-project-planning