Sea-level changes during the Pleistocene is a very sensitive subject because we cannot generalize any situation. As far as I know, sea-level changes due to the ice sheets have greater effect in inner seas like Black Sea, and smaller effects in the oceans. Level of the Black Sea was very low in the glacial maximum. But at that time, there is not such big change in the sea-level at the Persian Gulf because of its connection with the ocean.
Of course there are some changes all around the world. But they are not the same everywhere.
Possible origin of the Noah story, is just a speculation. It has no relation with the modern science. Recent researches in the sea of Marmara, showed alluvials at the southern part of the Bosphorus. That means the "big flood" did not existed in the Black Sea area. There are some excavated Bronze Age sites in Bulgarian Black Sea coast. But there are much more all over the world. All settlements of the fishers before 5 thousand years are underwater now.