If my opponent has an Empoleon V with "Emperor's Eyes" Ability active, and I have both an Eevee with a Memory Capsule attached and an Eevee with the "Resonant Evolution" Ability in play, if I evolve the Eevee with a Memory Capsule into a Jolteon with "Thunderous Awakening" Ability can I use "Resonant Evolution" or not?
Yes, that will work because Emperor's Eyes has been disabled.
Source: TPCi Rules Team (2022-10-06)
If I have multiple Eevee with "Resonant Evolution" in play, can each of them trigger if I evolve one other Eevee? Or do I have to evolve a separate Eevee for each one?
If you have multiple Eevee in play, playing a card from your hand to evolve 1 of them would trigger every Resonant Evolution.
Source: Astral Radiance FAQ; TPCi Rules Team (2022-05-26)