According to the Professional Scrum Product Owner II certification guide1, the Definition of Done is a formal description of the state of the Increment when it meets the quality measures required for the product.
The Definition of Done creates transparency by providing everyone a shared understanding of what work was completed and what standards were met as part of the Increment. If the Definition of Done is not met, the Increment is not Done and cannot be released. Therefore, the following statements are true:
A: The next Sprint may be interrupted when quality issues are encountered. This is true because the Scrum Team may have to spend time fixing the quality issues in the previous Increment before working on the new Sprint Backlog items. This may affect the Sprint Goal and the delivery of value.
C: The indication of progress on the Product Backlog is not transparent. This is true because the Product Backlog items that were supposedly Done in the previous Sprint are actually not Done according to the Definition of Done. This means that the Product Owner cannot accurately forecast the release plan and the stakeholders cannot trust the progress reports.
D: The Scrum Team should not release the Increment. This is true because releasing an Increment that does not meet the Definition of Done may compromise the quality, usability, and value of the product. It may also damage the reputation and trust of the Scrum Team and the organization.
E: The incomplete Sprint Backlog items should be returned to the Product Backlog. This is true because the Sprint Backlog items that were not Done according to the Definition of Done are still part of the Product Backlog. The Product Owner should re-order them based on their value and priority and decide when to include them in the next Sprint.
The following statement is false:
B: The project manager cannot effectively update the plan. This is false because there is no project manager role in Scrum. The Product Owner is responsible for managing the Product Backlog and the value delivery, while the Scrum Master is responsible for facilitating the Scrum process and removing impediments. The Developers are responsible for managing the Sprint Backlog and the quality of the Increment.
References: 1: Professional Scrum Product Owner II Certification | Scrum.org