An ability that triggers when a player casts a spell resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

If a card you discard has in its mana cost, X is considered to be 0.

The emblem created by Narset's last ability is colorless. The damage it deals is from a colorless source.

Because it's a loyalty ability, Narset's first ability isn't a mana ability. It can be activated only any time you could cast a sorcery. It uses the stack and can be responded to.

You can discard a card even if Narset leaves the battlefield before her middle ability resolves. The reflexive triggered ability will still trigger if you discard a nonland card.

Narset's second ability goes on the stack without a target. While that ability is resolving, you draw a card and may choose to discard a card. When you discard a nonland card this way, the reflexive triggered ability triggers and you pick a target to be dealt damage. This is different from effects that say "If you do . . ." in that you choose a target after looking at the card you draw and players can respond to the reflexive triggered ability knowing how much damage will be dealt.