A: If you are the active player, counter-Surprising does not use up one of your total plays for the turn. By the same token, however, this means you cannot use the Surprise for it’s function which would use a play. To wit:

You can only use a Surprise to do one of 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,
2a) on another player’s turn to cancel a play
OR
2b) on your turn to counter their interruption of your own play (“counter-Surprise”)

You cannot do more than one of those things.

So if you’re using it to counter-Surprise on your turn (2b), you can’t also use it as one of your plays for it’s “in-turn” function (1).