Question, do you have to discard your in-play cards BEFORE you discard your hand? I've always been under the impression that you discard all cards in any order, and this would allow you to keep an in-play card on top of your discard pile so that your opponent doesn't get to see any of the cards from your hand. The first quote sounds like you can do either order, the second quote could be interpreted that you have to do in-play cards first.
In the end the rulebook should be clearer and also as lax as possible. Man just get them discarded. The order of the discard pile will never matter except for people being able to see the top card. I imagine when I get the chance, I will have the rulebook let you discard hand or play cards in either order.
You do discard cards from play in a particular order, one at a time, which matters for things like Scheme; however obv. in practice when no such cards are around, just scoop 'em up. And as a result of these cards, you technically don't intermingle discards from hand and from play.
You are not required to pause anywhere in there to show people a card from your hand. Cards from hand are discarded all at once, so they never see more than one card.