Yes, the discard pile is face up. This is standard in almost any game, unless the rules specify otherwise. While the rulebook for Bang! doesn't seem to specifically state this either way, it does say that brown-bordered cards are
played by putting them directly into the discard pile and applying the effect described with text ore symbols on the cards".
This wouldn't make sense if the discard pile were face-down, as you wouldn't see the card that was just played if that were the case.
And yes, if someone is discarding multiple cards at once, they could put the least helpful card on top to try and hurt Pedro Ramirez. However, it is not common that a player will actually be discarding many cards at once; most cards that go into the discard pile go there from being played. Only if you have exceeded your hand limit at the end of your turn would you be discarding more than 1 card at a time.