Heretical "Hymns"

Hi,

I'm curious about two Hymn-related items.

The first is more theorical: What makes a hymn, a hymn, and not just a song or a tune?

Also, I've been told that "Amazing Grace" is heretical. The understanding of grace is not in line with Catholic theology. It's sort-of a form of pelagianism.
Are there other "hymns" that are heretical, or leading to heresy? I'm perhaps overly cautious in not singing in church, because I don't want to sing heresy.

Any help would be greatly apprciated.

-Mark