You can't argue with success. Your pizza looks fine. I will have to try it sometime.
I agree with most of what chiguy has said except for point number 4. I took "FP" in your post to mean food processor. If that's the case, I would put all the dry ingredients in the bowl first and then add the liquids, putting the oil in last. If you put the liquids in first and then add the dry ingredients, everything will splatter all over the inside surfaces of the bowl and will have to be scraped off. Also, the almost-liquid dough can get under the blade and crevices and gum up the machine. Using a stand mixer, I would basically reverse the process along the lines mentioned by chiguy. I personally don't put salt, sugar or oil in with the yeast and water while the yeast is being proofed. You can get away with a pinch of sugar with the ADY while it is being proofed, but that is far as I will go. You didn't indicate whether you were using ADY, but I assumed so from the fact that you proofed it.
As chiguy noted, you didn't indicate how much flour you used. But if you used 2 cups of water and 1/2 cup oil, I would estimate that you used something close to 6 cups, which would get you close to 60% hydration, which would be a workable hydration ratio for all-purpose flour. I suspect you don't measure out the flour because, with a food processor, it is easy to tell when there is enough flour since a nice dough ball forms just at the point where the amount of flour is just right. The downside of a food processor is that it produces a lot of heat in the dough because it has a high frictional heat component, about 3 to 4 times what a standard home stand mixer will produce. To mitigate the heat effects on the dough, I usually use cold water out of the refrigerator (and sometimes even ice water in the summer) and use mostly the "pulse" feature and, occasionally, the "on" speed, but for the shortest time possible (usually at the end of the knead cycle). I also tend to go right to the refrigerator with the dough so that it cools down as fast as possible.
At 1/2 cup oil, I would estimate that you are at around 5% (by weight of flour). That will show up in the crust in the form of a soft and tender crumb. Some thin crust pizzas, especially the ones with soft crumbs, can tolerate even more oil than you used. That is a characteristic, for example, of many of buzz's deep-dish doughs that he also uses for thin-crust pizzas. Some of the versions I made included over 10% oil.
I was most curious about your procedure of removing the heated stone (I assume it is at least 16 inches or better) and then putting the rolled out dough on it to par-bake. I wouldn't trust myself to do that safely, although my recollection is that fellow member friz78 uses a technique similar to yours (i.e., removing the stone with the baked pizza from the oven). I took your procedure to mean that you don't have a wood peel but that you may have a metal peel, which you use only to remove/replace the pizza once it sets up and bakes in the oven. I am speculating here but maybe you can clarify.