Does correct Breathing reduce stress, tension and even pain?

Yes. Using Abdominal Breathing to Reduce Stress and Pain is a fact.
A common reaction to stress is a tendency to take short and shallow breaths, and sometimes even to hold one's breath. When you do this, you may subconsciously feel that by holding your breath you will be able to better control the situation. The reverse is true. You are likely to have even greater stress and anxiety, to say nothing of having less oxygen.