Dough temp before oven

As far as I am aware (even after a quick search online), no. It’s an easy modification that everyone would probably be doing if it were helpful, but most people don’t do it. Some people even put their loaves in the freezer for half an hour or so to make them easier to score.

That's a complicated question based on too many individual variables, unique to your dough and baking environment and steps.  I usually only bench proof after shaping (rather than popping immediately into the fridge) if the dough feels or looks a little under-fermented during shaping.  You can do a finger poke test right after shaping to give you an idea as well.  If I've stretched out the bulk ferment precariously long, I will utilize the freezer for 15 mins prior to the fridge to try to put the brakes on.  Oven spring is also impacted by dough tension and shaping, so if you aren't building enough gluten before or after the fridge, the bench proof might actually be detrimental.  I've read many threads on this site and the web and it seems there are various schools of thought on the post-fridge bench warming.  I think you should probably just experiment and see what that variation does for your bake.  If your dough was under-fermented before going in the fridge, maybe the post-fridge bench warm might help.  For my formulas, the cold dough hitting the really hot oven and DO helps the dough spring up.  But, again, everyone's dough, oven, DO, etc are different and unique, so universal truths can be hard to come by.  If you try experimenting, I hope you will report back your results though and keep us posted!