With regard to you first example, it is not a question of that from a local CAA or EASA might be OK with just an EASA licence, rather that under EU law only requires the pilots of EU operated aircraft to have an EASA licence. The Convention only covers international aviation and gives no rights to aircraft registered in one contracting State to be based in another Contracting State or to make internal flights within the State. The licensing requirement is a condition which permits EU residents to base third country aircraft in the EU and undertake internal flights.
So far as your second example is concerned I think that you have misunderstood the scope of the licensing requirements. So far as third country aircraft opereated by EU residents are concerned, an EASA licence is only required if the flight begins, ends or takes place wholly within the EU. Once outside of the terriotry of EU member States the EU licensing requirements have no legal force and pilots with need to comply with requirements or the state of registry.
With regard to your third example, the legislation is quite clear and there is no requirement to have an EASA licnence in the circumstances you describe as no part of the flight would take place within the EU.