Puff pastry should not be kept in the fridge for too long (in spite of the vinegar), 2 or 3 days maximum. But it can easily be frozen, in which case don't do the final double turn and freeze at this stage. When needed, remove from freezer, leave to thaw in the fridge overnight, and do the final double turn just before use.
You wonder how-many layers there are? Here is the solution: after the first turn there are 2 butter layers between 3 dough layers, and each double turn multiplies by four. So after the first one we get 12 layers, 48 at the second, and 192 at the third.
How does it work? In the heat of the oven, the layers of pastry cook and turn brown and crisp, at the same time the butter melts (helping pastry to brown) and the water inside turns to steam. This steam in trapped in the pastry, so the entire pastry inflates to become puff pastry.