Can demons curse each other? Or does it not work as they're resistant to "dark affinity" damage? Same for angel blessings.

Demons can curse each other, and angels can bless each other - it just doesn't necessarily work very well. A demon cursing a demon is likely to have the result of a mild irritation rather than any real impact. In the same way, an angel that blesses another angel won't give that much more of a benefit.