Two excellent questions.
As to your first question, professional pizza operators use coolers that operate at around 35-40 degrees F. That's about 10 degrees lower than I can get out of my home refrigerator, but there are some home refrigerators that can get down to around 40 degrees or so. Some members of our forum have devised different ways of getting the dough to cool down faster. Canadave uses a metal container for the dough, which cools down faster than plastic or wood because heat conducts away faster from metal than other materials. Giovanni puts his dough in the freezer for a period of time. For a dough ball for a 16-inch pizza, I myself have tried Giovanni's approach and have been able to get away with around 30-40 minutes in the freezer without having the dough start to freeze. Most of the time I just put the dough in the refrigerator in a plastic bag and let it go at that.
As for your second question, the technical answer is that the time that it will take for the dough to reach the desired temperature for shaping, etc., depends on the temperature of the dough when it comes out of the refrigerator and the temperature of the room in which the dough is to sit before shaping. Newton's Law of Cooling, which also applies in reverse to heating, says that the temperature of an object changes at a rate proportional to its temperature and the temperature of its surrounding environment. To calculate that rate of change you need a starting temperature and some other data points that, with a scientific calculator and understanding how to use differential equations, you can actually calculate how long it will take for the object (such as a dough ball) to reach a particular temperature. Tom Lehmann says that the dough should be above 50 degrees F to shape without running the risk of bubbling. Since your dough is likely to be at a higher temperature coming out of the refrigerator (if your refrigerator is anything like mine) than a dough coming out of a professional cooler, it will take your dough less time to get above 50 degrees F than where a cooler is used.
I personally shoot for a temperature of between 55-60 degrees F. Obviously, the time to reach that temperature will be shorter in summer than in winter. But one way to do a rough calculation is to see how fast the temperature rises in a fixed period, such as a five minute period, and use that figure to extrapolate out to the desired temperature. The process is exponential rather than linear, but it will be close enough for your purposes over a 1-2 hour total time period. So, for example, if the temperature of the dough coming out of the refrigerator is at 50 degrees F and you are shooting for 55 degrees F, and the temperature rises 1 degree within the first 5 minutes, it will take roughly 50 minutes for the dough to reach 60 degrees F. I chose the numbers for this example for simplicity of the math, but, in actuality, at this time of year, where cooler room temperatures prevail, the rate or increase is much slower, more like 0.5-0.6 degrees F over a 5 minute period. To get a more accurate figure you will have to learn how to implement the math of Newton's Law of Cooling. Most bakers simply learn through experience in making doughs at different room temperatures throughout the year.
FYI, the optimal finished dough temperature used to be 85-90 degrees F. But, as cooler technology improved and coolers became more efficient, the optimal finished dough temperature was dropped to 80-85 degrees F. So, unlike Newton's Law of Cooling, it is not a natural law.