Why is trade openness positively correlated with economic prosperity? Is there any confirmed saying on this problem?
In short: Yes and due to comparative advantage.

The level of GDP growth gained with opening trade does vary by country and time. I'd suggest Wacziarg &amp; Welch (2008). Trade Liberalization and Growth: New Evidence, World Bank Economic Review, vol. 22(2) for a relatively new study on the subject.