You can select the card you discarded for the cost of “A Feather of the Phoenix” to be the card returned to the top of your Deck. If you discarded “Night Assailant” or “Makyura the Destructor”, then their effects will activate.
You can select a Fusion Monster in the Graveyard for “A Feather of the Phoenix” but it is returned to the Fusion Deck.
Discarding 1 card is a cost to activate this effect. Your opponent can chain “Disappear” to the activation of this card and remove the discarded card from play so that you cannot return it to the top of the Deck.