"Are Product Management questions on or off-topic at PM.SE?"
As it stands, the best (and latest) answer for this question is available on THIS ANSWER from Todd.
I share the TL;DR excerpt here:
Product management as it relates to project management is certainly on-topic here, but other aspects of product or portfolio management are out of scope. In particular, the roles and responsibilities of a Product Manager within a given project-management framework are likely to be very much within the scope of this site.
The on-topic session of our community has been expanded to make it explicitly clear.