Staryu

If Voltorb is attacked by Blastoise EX's "Rapid Spin" which pushes it to the Bench after doing damage, do you still flip for Voltorb's "Destiny Burst" Ability or not?

Yes. Destiny Burst checks for two things: Voltorb was damaged by an attack while it was your Active Pokemon, and Voltorb was Knocked Out by that attack. So even though you don't check for a KO until the attack is completed, the criteria for using Destiny Burst has been met, so it can be used. This holds true for any similar Ability that triggers when the Pokemon is Active and gets damaged by an attack.

If Gastly attacks with "Little Grudge" and on the next turn is KO'd by Blastoise-EX's "Rapid Spin" attack, does the Energy get discarded from Blastoise EX or from the Pokemon that replaces it? Neither?

Blastoise EX was the "attacking Pokemon", so it loses an energy.