During the second quest step, the card says that you have to destroy every card which heal Wilyador.

Does Elrond effect count as a "healing card" ?! Do you have to destroy it ?

Yes.

Be careful of even using a healing card with Elrond as your hero. He has a Response effect which takes place whenever a character is healed. AKA, it's not optional.

"Response" effects are optional; "Forced" effects are compulsory.