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.
Puff pastry is a laminated dough, with very strong gluten development, so an extra couple of days in the refrigerator should not have caused problems.
450 F seems like a typical temperature, and the time seems in the normal range.
The only thing you have mentioned is that is definitely outside the standard treatment is trimming the edges with a butter knife. Normally, you want to trim or cut puff pastry with a very sharp knife or pizza cutter, in order to cleanly cut through the layers. A blunt knife like a butter knife can mash the layers together, making it hard for them to separate at the edges of the pastry.
Still, this should have lead to lopsided or strangely risen pastry, rather than a complete failure to rise, especially in the center.
The other possibility is that the dough was too warm when you rolled and worked it, or that you rolled it too much, which would work the fat or butter layers into the dough phase, rather than keeping discrete layers of flour then fat, which is what allows the rise.
Best Answer
Yes, is possible, and not uncommon. You may wish to dock it to prevent excessive rising.
Some pastries are made with puff pastry that is already baked separately, such as the famous Napolean or Mille-Feuille . For example, in this recipe (which uses commercial puff pastry), the instructions are:
I cannot endorse the plain brown paper idea, but the method is fairly standard.
Here is another example, from King Arthur flour, of croissants du patisserie, which is essentially puff pastry baked as a croissant (as opposed to croissants du boulanger, the baker's croissants, which are yeast raised as well as a laminated pastry).