When a player leaves the game, any Auras attached to that player will be unattached from that player (C.R. 701.3d) and will be put into the graveyard as a state-based action (assuming that player neither owns nor controls them) (C.R. 704.5m). Therefore, if you own an Aura card put into your graveyard this way, you can return it to the battlefield with Faith's Reward or Second Sunrise, provided it was put there "this turn" and provided you will get priority again "this turn" (C.R. 116.1a).
Note that the Curse subtype (C.R. 205.3h) has no abilities or game mechanics inherent to that type, including the mechanic of enchanting or targeting a player.
800.4i If a player leaves the game during his or her turn, that turn continues to its completion without an active player. If the active player would receive priority, instead the next player in turn order receives priority, or the top object on the stack resolves, or the phase or step ends, whichever is appropriate.
Since the eliminated player’s turn continues, only without the eliminated player passing priority, there is time to cast faith’s reward and second sunrise before the turn ends. The aura’s returning to the battlefield after casting faith’s reward orsecond sunrise are attached to any legal target chosen by their controler
Question #1- Does eliminating a player from the game and Faith's Reward work with bringing Curse cards back into play?
Question #2 - If a player dies on their turn, is there an opportunity for me to cast Faith's Reward before the next turn to get back the curses?
An enigma as vexing as life itself.
Note that the Curse subtype (C.R. 205.3h) has no abilities or game mechanics inherent to that type, including the mechanic of enchanting or targeting a player.
EDIT (Feb. 26): Add rule citation.
Since the eliminated player’s turn continues, only without the eliminated player passing priority, there is time to cast faith’s reward and second sunrise before the turn ends. The aura’s returning to the battlefield after casting faith’s reward orsecond sunrise are attached to any legal target chosen by their controler