FAQ
I used this [Activate: Main] effect to play an "OP04-082 Kyros" from my hand, and then gave 1 of my opponent's Characters with a cost of 3 −2 cost. Can I use the [On Play] effect of my played "OP04-082 Kyros" to K.O. my opponent's Character that has been given −2 cost?
Yes, you can.
What happens if I choose my "OP04-082 Kyros" as the Character to K.O. according to this [When Attacking] effect, and then rest my Leader or [Corrida Coliseum] instead of K.O.'ing it?
Your "OP04-082 Kyros" will not be K.O.'d, and you will not be able to give 1 of your opponent's Characters −5 cost according to this [When Attacking] effect.
Can I activate this [On Play] effect and choose not to trash a card from my deck?
No, you cannot.

