Ill-Gotten Gains: Timing and Card Selection

[Nehptis]

1) When a player resolves Ill-Gotten Gains do all players simultaneously return 3 cards from their graveyards?  Or does the active player choose first?

2) Does each player reveal the returned cards to all players?  Or can each player pickup their graveyard, select 3 cards, and then return the rest to their graveyard.  Therefore, it would be up to the other player(s) to remember what was in the other graveyards to begin with.

[Limbo]

103.4. If multiple players would make choices and/or take actions at the same time, the active player (the player whose turn it is) makes any choices required, then the next player in turn order (usually the player seated to the active player’s left) makes any choices required followed by the remaining nonactive players in turn order. Then the actions happen simultaneously. This rule is often referred to as the “Active Player, Nonactive Player (APNAP) order� rule.
Example: A card reads “Each player sacrifices a creature.� First, the active player chooses a creature he or she controls. Then each of the nonactive players chooses a creature he or she controls. Then all creatures are sacrificed simultaneously.

This answers question 1 (which means yes and yes on both questions).

217.4b Each graveyard is kept in a single face-up pile. A player can examine the cards in any graveyard at any time but can’t change their order.

As the graveyard is viewable to all players, I assume common sense dictates that the chosen cards are shown to all players. I assume a judge will back me up on this one.

[epeeguy]

As the graveyard is viewable to all players, I assume common sense dictates that the chosen cards are shown to all players. I assume a judge will back me up on this one.

Correct.  Even if the instruction was "Return one card from your graveyard to your hand.", all players in the game would still be aware of which card was chosen before it was actually returned to the player's hand.  There does not need to be any wording that the card is "revealed", as it was never hidden in the first place (since the contents of the graveyards of both players are  public information).