Mimic says "This card counts as a duplicate of that card as if it just had been bought".
So I would say you discard the Mimic card if you decide to use those abilities (the other player's card remains). Perhaps not the best use of Mimic.
Ahhh, that makes senses.
If the copied card is used by the other player first and thus leaves play, then you can choose a new card to Mimic as explained in the rulebook blurb about Mimic.
My question about " Psychic Probe" is actually similar to the "Plot Twist" question which you've already graciously answered.