Permanent cards that were put into your graveyard from anywhere else, such as a card that was discarded, stay in the graveyard. Permanent cards that you gained control of and went to another player's graveyard from the battlefield will likewise stay in the graveyard.

You choose what an Aura card put onto the battlefield this way will enchant. You can't choose any permanent cards entering at the same time as that Aura. If there's nothing legal for the Aura to enchant, it stays in the graveyard.

A permanent card is a card that could be put onto the battlefield. Specifically, it means an artifact, creature, enchantment, land, or planeswalker card (instant and sorcery cards aren't permanent cards).

Permanent spells that were countered earlier in the turn never entered, so they won't return to the battlefield because of Faith's Reward.