There is no such thing as an accurate measurement in the sciences. That's why in an experiment you take many measurements and then calculate an average.
Yes, but there is little or no effort among quantum physicists to determine whether these fantastically precise predictions actually mirror reality. I don’t see how you can call it a settled question that quantum physics is correct until someone actually does such a study. If the actual experimental parameters only loosely approximate what they claim are highly precise theoretical predictions, then one would have to wonder whether they’ve got it right.