Can a player decide not to show cards which are discarded (for example: effect of lost intrigue challenge, Rule by Decree , The Hound... ) and simply put them face down in the discard pile?

And by the way: can a player ask opponent to show him his discard pile/dead pile so that he could refresh his knowledge about all the opponent's cards that are already discarded? Is this an information that is clear for everyone all the time (just like the player can ask about the number of cards in opponent's hand)?

If I remember properly, you are have the right to go through enemy's dead pile/discard pile at any moment, as they are stacked face up... I can't recall the exact place where I read such a thing, but I'm quite certain

FAQ page 8,

(3.30) Dead and Discard Pile
You may not change the order of cards in your
discard or dead pile. You may look at any
player's discard or dead pile at any time.