They all can theoretically be a reason to buy a copper or curse?
no, but you're close
They are all cards that can be reasons to prefer a card to be a curse rather than a copper.
yay
I don't see how that fits for Apothecary, Mine, or Moneylender.
1. ApothecaryThere are 2 colonies left in the supply. You need both of them to win, and you need to buy them this turn and the next turn, or you will lose. Your hand is 5*apothecary. Your discard pile is 5 Estates; your draw pile is 11 Coppers. On top of your deck is: Platinum, Platinum, Copper, Copper, (XXX), Colony, Colony, Colony.
Case 1: XXX is a copper.
You play apothecary. You draw Platinum, Copper, Copper, Copper, and put Platinum on top of your deck. Your hand is now: 4*apothecary, Platinum, 3*Copper. That's not enough coin, so you need to play the other one. You play apothecary. You draw Platinum, reveal 3 Colones, shuffle, and reveal one Estate. You put these on top of your deck. You have 13$ and buy a colony. In your Cleanup, you draw 5 Estates.
Your opponent has his turn, it's a dead turn. Your turn again, your hand is 3*colony 2*Estate. You can't do anything, you give up your turn. on your next opponent's turn, he buys the last colony.
Case 2: XXX is a Curse
You play apothecary. You draw Platinum, Copper, Copper, and put Curse and then Platinum on top of your deck. You play the second Apothecary, you reveal Curse, Colony, Colony, Colony. You put these on top of your deck in any order. Your hand has 12$ and you buy the colony. In your Clean-up, you draw 3*Colony, Curse, shuffle everything, and draw apothecary.
On your opponent's turn, he has a dead hand, so you get another turn.
You play apothecary. You draw apothecary + 4* copper. You play apothecary, you draw Apothecary + 4*Copper. You play apothecary, you draw an Estate + 4*Copper. You buy the colony and win.
2. MineYou are 4P behind, and the last Provinces is the only Victory card left in the supply. The copper pile has 2 cards in it, the silver pile one. Your hand is: Mine, 3*Estate, XX. In your turn, you missclick and play Mine (I know, bad solution, but otherwise you need another Action card to make it work). If it's copper, you have to trash it and either end on a 3pile (silvers, duchies, estates), or take the copper and allow him to end on a 3-pile with coppers. you could have bought the province next turn!
3. MoneylenderIf you really need a card because it will allow you to trash it with forager which will give you +1 buy and allow you to buy another colony or something. Needs other Action cards.
#2 and #3 could be cut. Apothecary is legit though.