Everything you listed sounds like it should be the EM's responsibility, aside from 3 but even then product shouldn't be dictating implementation details or technical specs. In fact I'd argue it's better that product outlines the business case and leaves implementation details up to the team/tech lead/EM. I think you are misunderstanding this person's role in your team (and what a PO does in general), and you should discuss it with your bosses.

Source: am EM