Very Short Explanation: According to Scrum.org, the Product Owner is not required to create clear and unambiguous acceptance criteria for each item in the product's backlog before it can be selected in Sprint Planning1. Acceptance Criteria is optional and is not prescribed by Scrum12. It can be valuable, but it's not a must12. The Developers can inspect and adapt the Sprint Backlog in any way they see fit, in order to help meet the Sprint Goal2.

One of the possible indicators that a Product Owner needs to work more with the Scrum Team is when the Increment presented at the Sprint Review does not reflect what she thought she had asked for. This means that there is a gap or a misunderstanding between the Product Owner and the Developers regarding the Product Backlog items, the acceptance criteria, the Definition of Done, or the product vision and goals.
The Product Owner is accountable for maximizing the value of the product resulting from the work of the Scrum Team. The Product Owner is responsible for managing and refining the Product Backlog, collaborating with the stakeholders and the Developers, and ordering the items in a way that best achieves goals and missions. The Product Owner represents the interests of everyone with a stake in the product and ensures that the Scrum Team works on the right things at the right time.
The Developers are accountable for creating a "Done" Increment that meets the Definition of Done each Sprint. The Developers are responsible for planning and executing the Sprint Backlog, designing and building the product functionality, testing and improving the product quality, and delivering a potentially releasable Increment. The Developers work closely with the Product Owner to understand and clarify the Product Backlog items, provide feedback and estimates, and suggest improvements and innovations.
The Sprint Review is an event that occurs at the end of each Sprint, where the Scrum Team and the stakeholders inspect the Increment and adapt the Product Backlog if needed. The Sprint Review is an opportunity for the Product Owner to validate that the Increment meets her expectations and delivers value to the customers and users. The Sprint Review is also an opportunity for the Developers to demonstrate their work and receive feedback from the Product Owner and the stakeholders.
If the Increment presented at the Sprint Review does not reflect what the Product Owner thought she had asked for, it may indicate that there was insufficient or ineffective communication, collaboration, or alignment between the Product Owner and the Developers during the Sprint. This may result in wasted effort, rework, delays, or dissatisfaction for both parties. To avoid or resolve this situation, the Product Owner needs to work more with the Scrum Team by doing some of the following actions:
Engage in frequent and regular interactions with the Developers throughout the Sprint to clarify, refine, and review the Product Backlog items and their acceptance criteria.
Provide clear and concise descriptions of what is needed and why it is valuable for each Product Backlog item.
Involve key stakeholders in defining and prioritizing the Product Backlog items and their acceptance criteria.
Empower and trust the Developers to make technical decisions and trade-offs that best meet the product goals and quality standards.
Solicit and incorporate feedback from the Developers on how to improve or simplify the Product Backlog items or their acceptance criteria.
Inspect and adapt based on empirical evidence from testing, data, or customer feedback.
Reference:
Scrum Guide: https://www.scrumguides.org/scrum-guide.html
Sprint Review: https://www.scrum.org/resources/what-is-a-sprint-review
Product Owner: https://www.scrum.org/resources/what-is-a-product-owner
Developers: https://www.scrum.org/resources/what-is-a-developer-in-scrum

Explanation
The Scrum Team member who is accountable for creating a valuable and usable Increment each Sprint is the Developers. This is because:
* The Developers are accountable for creating a "Done" Increment in every Sprint. They must ensure that every Product Backlog item they work on meets the Definition of Done before it is considered complete.
* The Definition of Done is a formal description of the state of the Increment when it meets the quality
* measures required for the product. It is a shared understanding among the Scrum Team and the stakeholders of what "Done" means for any Product Backlog item that is selected for a Sprint.
* The Increment is a concrete and usable outcome of the Sprint that provides a measure of progress and value delivery. It must be in useable condition regardless of whether it will be released or not.
* The Developers are self-managing professionals who organize and manage their own work. They decide how to best accomplish their work, rather than being directed by others outside the Scrum Team.
Other options, such as the CEO, the Product Owner, the Scrum Master, or the Scrum Team, are not accountable for creating a valuable and usable Increment each Sprint. They may have different roles and accountabilities in Scrum, but they do not do the actual work of creating a "Done" Increment.
References:
* [Scrum Guide], page 7, section "Developers"
* [Scrum Guide], page 10, section "Definition of Done"
* [Scrum Guide], page 10, section "Increment"
* [Scrum Guide], page 7, section "The Scrum Team"

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"