Depends on the enchantment you use on your weapon.
Fire/Frost/shock damage will be affected by your destruction skills AND magicka cost reduction enchantment. I.E if you have 100% Fortify Destruction enchantments equipped, then your weapon will not use any charge. I think (has to be confirmed, maybe Dagmar can help) that Absorb enchantment also falls into the Destruction category (as Drain Life does).
Paralyze goes under Alteration though. Banish goes under Conjuration, as well as Soultrap and Fiery Soultrap. Fear is under Illusion and Turn Undead under Restoration.