Explanation
It is not true that the Product Owner must write all of the Product Backlog items (e.g. user stories, requirements, etc.) on the Product Backlog before handing them over to the Scrum Team. This is because:
* The Product Backlog is an emergent, ordered list of what is needed to improve the product. It is never complete and constantly changes to reflect the needs and desires of the customers, users, and stakeholders.
* The Product Owner is accountable for maximizing the value of the product resulting from the work of the Scrum Team. They are responsible for identifying and articulating the Product Goal, which is a long-term objective for the product that guides all the activities of the Scrum Team.
* The Product Owner is also accountable for managing the Product Backlog items effectively. They must ensure that they are transparent, visible, and understood by everyone who needs to work on them. They must also collaborate with the Developers and stakeholders to refine, order, and prioritize them based on value and impact.
* The Product Owner does not need to write all of the Product Backlog items by themselves or before handing them over to the Scrum Team. They can involve others in creating or contributing to them, such as customers, users, stakeholders, or Developers. They can also add or modify them at any time during the product development process, as long as they are clear and ready for selection in Sprint Planning.
References:
* [Scrum Guide], page 6, section "Product Owner"
* [Scrum Guide], page 11, section "Product Backlog"
* [Scrum Guide], page 10, section "Product Goal"
* [Scrum Guide], page 12, section "Product Backlog Refinement"
* [Scrum Guide], page 14, section "Sprint Planning"

Explanation
Cross-functional teams are not optimized to work on one component or layer of a system only. This is because:
* Cross-functional teams are teams that have all the skills and competencies needed to accomplish the work without depending on others who are not part of the team.
* Cross-functional teams are able to deliver value across the entire product, rather than focusing on a specific component or layer. They can work on any aspect of the product that is needed to achieve the Sprint Goal and the Product Goal.
* Cross-functional teams are more agile, collaborative, and creative than teams that are specialized or siloed. They can reduce dependencies, handoffs, and delays, and increase feedback, learning, and adaptation.
References:
* [Scrum Guide], page 7, section "Developers"
* [Scrum Guide], page 10, section "Product Goal"
* [Scrum Guide], page 7, section "The Scrum Team"