Does Narset, Enlightened Master's ability trigger twice if she has double strike, since she has an ability that says "When (she) attacks"?
The trigger, "Whenever ~ attacks" means "Whenever ~ is declared as an attacking creature". A creature with double strike will deal damage in the two combat damage steps, but will only be declared as an attacker once per turn. (Normally, unless some other effect is creating additional combat phases.)
No. Declaring a creature to attack only happens once per combat phase, no matter how often it deals combat damage.
There are some cards that grant you additional combat phases.
A creature with Double Strike would only trigger "on dealing (combat) damage" triggers twice.
Actually, it does count as attacking twice. According to the mtg wiki and some other referances, there is a first-strike attack phase and a regular attack phase. Take a look Here at the wiki. So, due to the fact that she is attacking twice, that power would be activated twice when you declare that she is attacking. If you do not believe me, take a look at some of these other questions where people have asked similar things:
Hope I helped,