If I use Pachirisu's "Electrified Incisors" attack and during their next turn my opponent retreats their Active Pokemon, is the new Active Pokemon still affected by Electrified Incisors?
No, it is not. Even though Electrified Incisors says "during your opponent's next turn" the effect of the attack is on the Defending Pokemon, not on your opponent. Retreating clears the effect.
Electrified Incisors