101.4. 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, in turn order, chooses a creature he or she controls. Then all creatures chosen this way are sacrificed simultaneously.

101.4a If an effect has each player choose a card in a hidden zone, such as his or her hand or library, those cards may remain face down as they’re chosen. However, each player must clearly indicate which face-down card he or she is choosing.

101.4b A player knows the choices made by the previous players when he or she makes his or her choice, except as specified in 101.4a.

400.2. Public zones are zones in which all players can see the cards’ faces, except for those cards that some rule or effect specifically allow to be face down. Graveyard, battlefield, stack, exile, ante, and command are public zones. Hidden zones are zones in which not all players can be expected to see the cards’ faces. Library and hand are hidden zones, even if all the cards in one such zone happen to be revealed.

That kinda ties into a question I have. If your hand is always revealed, perhaps as through the card mentioned above, does it mean you could cast cards such as Belfry Trap for free at anytime?

NGA Constructed rules questions probably belong somewhere else although I don't really know where

But then it doesn't work with Duress and friends, which I assume is the intent. "Revealed your hand" also has ambiguity: is it referring to your hand, the zone, or the cards in your hand?