Good question. I see Product Owner and Product Manager as fairly interchangeable, but it likely depends on the size of the organization. Larger organizations may keep Product Owners more focused on managing the day-to-day backlog & scrum team where Product Managers are more strategic and focused on the longer term product roadmap.
A user interface includes interaction & visual design. Again, larger organizations may have specialists in each discipline. I believe a capable UI Designer should be able to understand all aspects of designing a user interface — interactions, motion, visual aesthetic, branding, and at least a basic understanding of the underlying code and its capabilities.