Skill = anything that is not the basic left-click attack. Adding elemental damage to skills from equipment doesn't cause this passive to trigger, only when the skill itself is of the proper element, though that does take skill modifiers into account. So for example, Consuming Ember has a chance to trigger the meteor but not the frost lance or chain lightning even if you have lightning and frost damage on spells, but if you take the Fratricidal Reunification skill modifier for it then it'll trigger chain lightning instead as the skill's damage was converted from fire to lightning.

Wailing Arrows with the Flames of Envy modifier triggers Abanazaar's Accord (which seems right). But Stings of Kraerion with Whitefield Arrowheads to make Frost damage the main component of the skill damage does not trigger an accord. Is this a bug?

The same skills have the same interaction with Omnitempest - Wailing works, Stings does not. Is this because Stings is a projectile skill?

If this is not a bug, then how can a pure archer use these two passive nodes without being a dedicated fire build?