If I play a Stand on Fight on another player's ally, such as Riddlemark's Finest, then I exhaust and discard them to place two progress on a location, whose discard pile do they go? Mine, since I played Stand and Fight on them, or the other player's, whose deck the card originally came from?

Bonus round: If I play Defender of the West on another player's Landroval, and then use his Response while he is under my control, does he return to my hand or the other player's hand?

The Riddermark would go back to the original player's discard pile.

Page 6 of the online Rules Reference: When a card is discarded, it goes to the discard pile belonging to the card’s originating deck.

Landroval would return to the other player's hand.

Page 12 : A card’s owner is the player whose deck held the card at the start of the game.