A: If you are the active player, counter-Surprising does not use up one of your total plays for the turn. However, it does use up the card itself, putting it in the discard pile, so it’s no longer in your hand, available to be used for it’s in-turn function as one of your plays.

Basically, a Surprise can do one (and only one) of those three things:

1) use it on your turn as a play, for it’s in-turn function
OR
2) use it to Surprise another player during their turn
OR
3) during any players turn to counter a Surprise played in any of these three capacities, against you or any other player

One you use it for one of these functions, it’s gone.