Explanation
The metrics that will help a Product Owner determine if a product is delivering value are customer satisfaction and time to market. This is because:
Customer satisfaction is a measure of how well the product meets the needs and expectations of the customers5. It reflects the value proposition of the product and the feedback from the users.
Time to market is a measure of how quickly the product can be delivered to the market. It reflects the agility and responsiveness of the Scrum Team and the ability to deliver value early and often.
Other metrics, such as productivity, velocity, and percentage of scope implemented, are not directly related to value delivery. They may indicate how efficiently or effectively the Scrum Team is working, but they do not necessarily reflect how valuable or desirable the product is for the customers or stakeholders.
References:
Professional Scrum Product Owner Training, page 5, section "Product Value" Professional Scrum Product Owner Training, page 6, section "Product Vision" Professional Scrum Product Owner Training, page 7, section "Product Backlog Management" Professional Scrum Product Owner Training, page 8, section "Release Management" Professional Scrum Product Owner Training, page 9, section "Business Strategy" Professional Scrum Product Owner Training, page 10, section "Stakeholders & Customers"

Scrum does not require that the Product Owner must use any of the following items:
Burndown chart: A burndown chart is a graphical representation of work left to do versus time. It can be used to track progress and forecast completion dates of projects or Sprints. However, it is not mandatory or prescribed in Scrum. It is one of the possible techniques that a Product Owner may use to monitor and communicate product development.
Feature burn-up: A feature burn-up chart is a graphical representation of features completed versus time. It can be used to track progress and forecast scope changes of projects or Sprints. However, it is not mandatory or prescribed in Scrum. It is one of the possible techniques that a Product Owner may use to monitor and communicate product development.
Critical Path Analysis: Critical Path Analysis is a project management technique that identifies the sequence of tasks that must be completed on time for a project or Sprint to finish on schedule. It can be used to plan, monitor, and control complex projects or Sprints. However, it is not mandatory or prescribed in Scrum. It is one of the possible techniques that a Product Owner may use to manage product development.
Project Gantt chart: A project Gantt chart is a graphical representation of tasks, dependencies, durations, and milestones of a project or Sprint. It can be used to plan, monitor, and control complex projects or Sprints. However, it is not mandatory or prescribed in Scrum. It is one of the possible techniques that a Product Owner may use to manage product development.
Therefore, the correct answer is none of the above.
Reference:
[Scrum Guide], page 6, section "Product Owner"
[Scrum Guide], page 11, section "Product Backlog"
[Professional Scrum Product Owner Training], page 8, section "Release Management"

Explanation
Sprint 0 is a term that some organizations use to describe a phase of work before the first official Sprint, where they do some upfront planning, design, architecture, or analysis1. However, this term is not consistent with the Scrum framework, which does not prescribe any pre-Sprint activities or phases2. Scrum starts with a Product Backlog that contains at least one valuable and feasible Product Goal, and enough Product Backlog items to initiate the first Sprint[3][3]. The Product Owner is accountable for maximizing the value of the product and the work of the Developers, and for managing the Product Backlog4. The Product Owner does not have any specific accountability during Sprint 0, because Sprint 0 is not a part of Scrum.
References:
1: Sprint Zero: A Good Idea or Not?, Scrum Alliance, accessed on December 16, 2023
2: The Scrum Guide, November 2020, p. 5
[3][3]: The Scrum Guide, November 2020, p. 9
4: The Scrum Guide, November 2020, p. 6