What is the proper technique for making an angel food cake?

Answering your specific questions, since there's no way for us to know exactly how you did it just by linking to the recipe:

1. Confectioners' sugar has smaller granules than granulated sugar, which means that you actually get more of it in a cup than you do granulated. However, if you're making your batter properly, the sugar should completely dissolve, so if you're going by weight there should be no difference. (And you should be going by weight.)
2. Cake flour is much lower-gluten, so you get a lighter, fluffier texture. All-purpose flour has much more gluten and you'll end up with a chewier end product.
3. The proper temperature is that which will bring the center of the cake up to temperature before the exterior burns. In order to get your temperature just right you should preheat the oven well in advance and allow it to stabilize first; give it at least 15 minutes after coming up to temperature. Also, get a proper oven thermometer rather than relying on the one that's built-in to your oven, and if your temperature is particularly unstable you might consider doing the baking inside of a cloche or a Dutch oven (which needs to be preheated as well, of course). And, the time stated in the recipe is just a guideline - you should be keeping an eye on it and using a bamboo skewer or similar to test doneness, rather than just looking at the outside.

And one which you didn't ask about but which is a common problem:

1. When you fold the flour into the batter, do exactly that - fold it in, gently, so that you don't disrupt the airy texture. Don't stir it or mix it or whip it or anything else, and certainly don't overwork it.