Public knowledge in Settlers of Catan?
It is my experience that when players trade, the player who's turn it is asks for resources or offers them.  The other players will then respond to the proposed trade however they see fit.  All this information is done publicly and other players  may offer a better trade to undercut another player.  There isn't anything in the rules about trading having to be done publicly, but it's the only way I've seen the game played.  Also, if you play the game online on the games official website, all trades are offered publicly by a player requesting a resource, and the results of that trade is shown to all users.  The same goes for if the player chooses to trade with the bank.

Since the size of a players hand is public knowledge, (that is declared explicitly in the rules) when they discard cards, how many cards they've discarded is also public knowledge.  You can watch them return the cards to the bank, and make a accurate educated guess of how many cards of each type are returned.  Thus, while it's not in the rules for them to declare how much of what they're discarding, it's easy to guess most times.  On the online version of the game, that information is offered to the player.

Finally, how many cards are left in the bank is something that is mentioned in the rules.


  If there is not enough of a given resource in the supply to fulfill everyone’s production, then no one receives any of that resource during that turn.


Thus, during resource production, a count of how many resources are left in the bank of a particular type should be made if it looks like there will be a shortage.  I can't find reference in the rules if there are other times when the resource should be counted, but there is nothing in the rules saying you can't do it either.  However, in the official online implementation of the game, that information is NOT offered to the player.