I was just about to post when PizzaHog and Steve973 posted in fairly rapid succession. Rather than reworking my post to reflect PizzaHog's and Steve's observations, even at the risk of overlapping some of their replies, I will leave my post alone and attempt to answer your questions in the order in which you presented them.
1. Yeast. In general, and all else being equal, the longer you want to hold the dough balls in the refrigerator before using, the less yeast you should use, no matter the type of yeast. The New Faithful dough recipe you used calls for 1%. That is a lot of yeast, by any measure, even for a cold fermentation application. That means that at 1% you should expect the dough to rise substantially, even while in the refrigerator. Also, with 3% sugar in the recipe, you should have gotten a lot of fermentation activity over a period of over 44 hours. Using 2% salt rather than 3% salt should also have increased the fermentation rate somewhat but perhaps not enough to give credit to the lower salt levels for the overall results you achieved. If you want to learn more about the effects of salt on dough, whether it is pizza dough or any other type of dough, such as bread dough, see this piece on salt from King Arthur at http://www.kingarthurflour.com/professional/salt.html
. There is also a very good article on salt at http://www.pizzamaking.com/forum/index.php/topic,8764.msg75936/topicseen.html#msg75936
The extent to which the rim and the rest of the pizza will expand during baking is primarily determined by the amount of moisture in the dough (its hydration) and the rate at which that moisture leaves the dough during baking, the extent of yeast activity before the yeast dies during baking (at around 145 degrees F), the degree to which the rim of the dough is unmolested during shaping and whether the dough is cold or warm when ready to use, the mode of baking, that is, whether on a pizza stone, a pizza screen, or a pan/disk of some sort, and the oven temperature. All else being equal, the oven spring is likely to be best using a pizza stone, followed by a pizza screen and a pan/disk.
Overall, I would say that it was perhaps the high levels of yeast and the high levels of fermentation activity and the increased byproducts of fermentation that were primarily responsible for the difference in the New Faithful pizza as compared with your other pizzas. Using KABF instead of Better for Bread flour, using less salt, and using a slightly higher fermentation percent (60% versus 58%) would not, in my opinion, account for the differences.
2. Sugar. Sugar is not an essential pizza dough ingredient. However, when used, as is the case with the New Faithful recipe you used, and depending on the amount used, it can have the multiple purposes you noted. In your case, when you used 3% sugar (sucrose), some of the sugar was converted to simple sugars for the yeast to use as food (yeast cannot use sucrose by itself, it has to be converted to simple sugars), and the remaining sugar, whatever its value, would have been available as residual sugar at the time of baking to contribute to crust coloration and oven spring. You might be able to taste the sugar in the finished crust, but that will depend not only on the amount of sugar that was used in the recipe to start and the residual sugar levels but also on your palate and your personal sensitivity to sugar. In addition to the multiple functions of contributing to taste/flavor, feeding the yeast and contributing to crust coloration, it is important to know that sugar is a hygroscopic substance (that is, it attract moisture from its surroundings). As a result, it will hold some water in the dough. That usually translates into a more tender crust and crumb. You can omit the sugar if you wish, since it is not an essential ingredient as noted above, but you will end up with a less tender crust and crumb and a dryer, more chewy one. Some members omit the sugar just for those reasons. If, in your case, you happen to like a crust that is on the sweet side, then that might contribute to your personal enjoyment of the pizza.
3. Oil. Oil serves several purposes in a pizza dough. It helps coat the gluten strands to improve the handling qualities, rheology (flow characteristics), and extensibility (stretchiness) of the dough, and it also helps provide flavor, which also depends on the type of oil used. However, the oil also serves to reduce the degree to which moisture in the dough leaves the dough during baking. As a result, the oil will help produce a softer crust and crumb. If you want an especially soft and tender crust and crumb, you should use both oil and sugar. That is behind the crusts of the major chains, like Papa John's and Domino's.
4. The rim of the crust. I would say that most pizza operators leave a space of about an inch from the perimeter of the pizza. Some will intentionally spread some shredded or grated cheese on the rim because they like the effect of baked cheese on the rim, but the toppings are kept out of that one-inch zone. There are some pizzas that are essentially rimless and where the cheeses and toppings can go right out the end of the pizza, but that is not the style of pizza that the New Faithful dough recipe is intended to make.
5. Temperature. You have pretty much answered your own question on this one. There are so many different oven designs and oven configurations and so many different baking protocols (e.g., pizza stones, screens, and pans/disks) that is is impossible to generalize on this matter. Also, not all dough formulations can be baked the same way in all ovens or oven configurations. You learn either from analyzing oven thermodynamics or through experience and trial and error.
6. Hydration. Hydration is usually determined by the rated absorption of a flour. For example, for the KABF, it is around 62%. I would imagine that it is the same for the Better for Bread flour. However, many professional pizza operators use around 56-60% hydration. Many artisan pizza makers often use higher hydration levels, maybe up to 65% for the two flours mentioned above. Higher hydration levels will usually produce a more open and airy crust and crumb. It is usually not associated with producing more flavor, but I suppose that someone might like the taste of a more open and airy crust and crumb better than a denser one.
I look forward to seeing the photos once your wife returns with the camera. While we are waiting, can you describe the "awesome" sauce that you made and enjoyed so much?