When I started learning Swedish I looked up a bunch of Swedish songs, this one is my favorite =D
Is there a distinction between "hero" and "heroine" in Swedish, or is hjälte used for both genders?
You can say hjältinna if you really want a feminine form, but my impression is that it's used less in Swedish than in English. In this context it would sound a bit odd to me, but if you're talking about the heroine of a book, hjältinna would be ok (though I'd still prefer hjälte in most if not all contexts).
It's not used that much in English either. You would not tell someone they are your heroine.