Before you tackle too much - take a multi meter, disconnect the battery negative and then the positive, then check for continuity from the alternator charge output to the battery. If you've got a very low resistance, then it's not an open.
And it's not a short - *pet peeve* You're looking for an OPEN. An OPEN is where current doesn't flow where it should; a SHORT flows current when it SHOULDN'T. A SHORT would be letting smoke out and making a fire ...
RwP