How to keep frozen puff pastry dough keep its shape

Looking at this recipe I don't see any reason why you couldn't use puff pastry as the container.

The only ways that the preparation would be different is:
puff pastry doesn't dry out as fast as filo so you don't have to worry about the wet towel in the instructions.
You wouldn't want to do multiple layers of puff pastry as the recipe calls for. You would just form a single pouch to hold your filling and seal it well.

Know that the texture will be different of course. The filo will be a bit more crisp and the layers larger and more distinct- filo is also a lot more work. You may find that the baking time needs to be adjusted a little but I don't think it will be very different if at all. Cook them until they're golden using the recipe's time as a starting point.

This recipe is in a Mediterranean style and filo would be more traditional but puff pastry would produce something tasty.

No, you don't have to freeze it at all.

The recipe you linked is indeed for puff pastry. It is rather tedious to create it, so it is available in supermarkets as a pre-fabricated food, just like pizza dough and other doughs. But it doesn't have a long shelf life in the fridge, so it is sold frozen. The recipe assumes that you will buy it frozen, and warns you to let it come to room temperature before you start baking.

If you are making your own, the end product can be used in cookies immediately. Just pay attention to follow proper technique and work with a very cold dough and butter while making the puff pastry. The link you posted probably explains it - if not, search for better instructions.