Also, could I use a Surprise that was part of the subturn to cancel the attacking Surprise, and if so would that count as one of the plays?

Example:
Player #1 plays “Draw 3, Play 2 Of Them” and gets an Action, a Keeper, and a Surprise.
They play their Action and Player #2 plays Belay That [Avast, Stop That] to cancel it.
–> can Player #1 use the Surprise in their mini-hand to cancel that Surprise,
–> and if so do they still get to play their Keeper afterwards?

A: Yes, you can use a Surprise from your main hand, or from your sub-hand, to cancel another player’s Surprise during your Draw 3, Play 2 Action. Playing a Surprise to cancel a Surprise is a free action, so yes, you would get to play the third card if your second card is a Surprise that you use to counter a Surprise being used to stop your first card.

Using Goal Bonanza also results in the play of a “sub-hand” while the rest of your hand is put aside, and the same things would apply there as well. Yes, you can counter-Surprise from either your main hand or your sub-hand.

In the case of Fizzbin, you don’t have the option of using any of the cards in your temporary hand, you have to play them blind, in random order, so any Surprises that are in that temporary hand won’t be useful to you – but you can still use Surprises in your set-aside hand to counter Surprises played against cards played as part of your Fizzbin action.