Do these cards make the resources generated by the hero they are attached to multi-color resources or does the hero generate one resource of each sphere?

They make them multi-colored resources.

But does this mean the hero now generates 2 resources which are both multi-sphere or one resource which happens to be multi-sphere (assuming one Song was played on the hero)? Essentially, do the songs allow heros to generate more resources per turn, or just make their one resource more flexible?

One resource, more flexible.