Let me try and take a crack at it and others are more than welcome to add/correct:
All of our rooms are different temperatures but I would guess standard is somewhere around 72 degrees. Maybe a bit higher since it is usually a kitchen.
It is really not critically important. The important thing is to let the dough warm up to a temperature at which you can easily open and shape the dough. I have read Peter (Pete-zza) provide guidance that the dough ball should be at 56 degrees or more. If you get to at least that temperature, then you have a broad range (I guess 56 to 65) to work within.
Walk in cooler? You do not have one - so I do not think it really matters exactly what they use in a restaurant. But, your 34 degree home fridge (cooler than most I think, but fine) is fine and the 50 degrees you mentioned is not the answer temperature to use if your recipe calls for a cold ferment in a cooler.
I think I am saying there is no magic number for room temperature and the cold fermentation at 34 degrees is fine. Just make sure the dough balls warm up enough, 56 or more, and go from there.
2 hours, 4 hours? Go more by the temperature of the dough, as described and also by the visual cues that you already know about. Even when following a recipe, no one makes a dough exactly the same as another and no one has the same exact environmental conditions and equipment.
There is not an exact moment when the dough is ready. It is more of a period of time - the window of usability. The window is probably at least 2 hours if not several more.
So, if 2 hours was too soon (I do not think so since you said it was a bit over fermented), then try 3 or 4 and see how it goes. Hopefully, it should not take more than a couple of tries before you get close to what works for you, your recipe and your environment.
Beyond that, I am unclear what problem you are looking to solve. Help us know a bit more. Also, it may be helpful to actually tell us the recipe you are following. I remember you previously saying you were using the recipe from the Pizza Bible, but I do not know if that is still true.
Hope some of this helps.