The answer may depend on the nature of the project.
If the project is purely around delivery and technical implementation of a software product, then perhaps there is no place for a PM in the role that would be recognised within Prince 2 - although that is arguable, as I suspect that there are few projects that exist to deliver only software.
If, as may be more likely, the project encompasses substantial business change, procurement and implementation of hardware and software infrastructure, development and delivery of end-user training, financial management, project and programme reporting, risk management, and benefit realisation, alongside the software development, then I do believe that the PM has an important role.
The PM should not be the Scrum Master, in my opinion, nor should he be the Product Owner. The PM in Prince 2 can be quite divorced from the technical delivery. The role should focus on ensuring that the delivery teams know what they are expected to deliver, then keeping on top of risks, benefit planning and realisation, quality, and progress. In such a role, the PM may be managing several small projects simultaneously, or one large project that needs a high level of coordination and reporting.
Your question asks about communication to and from the PM: this should probably be with the Product Owner, who in Prince 2 terms could probably be considered as a Team Manager. You also ask about the level of involvement that the PM should have in day-to-day delivery: I believe this should be very limited indeed.