原文Archmage of Runes's first ability doesn't change the mana cost or mana value of any spell. It changes only the total cost you pay to cast instant and sorcery spells.
原文Archmage of Runes's first ability can't reduce the amount of colored mana you pay for a spell. It reduces only the generic mana component of that spell.
原文Archmage of Runes's last ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered or otherwise leaves the stack without resolving.