The climate would have had warm summers and brutal winters for any areas not under and ice cap. 15,000 years is 3000 years after the max of the ice age and 1000 years before the first of the great flooding periods. So ther may have been some coastal lowlands. It seems possible but not too likely for rice cultivation.
2. Most current thought put the gradual cultivation of rice moving from wild plants gathered by farmers to developed plants occuring in a semi-tropical or tropical zone. There is evidence for this on the Malay Penninsula and Korat Plateau in Southeast Asia between 8,000 and 8,500 years ago. The wide variety of plants available to the people fits a tropical setting. The Negritos on the Malay pennninsula first gathered plants near their villages and later cultivated rice. Their discoveries may have gone back as far as 10,000 years.
3. The great land mass in Asia that was lost in the sea level rise, did force people into current land areas in China and Korea as well as Southeast Asia but the first large move would have been 14,000 year ago. As life was easier in the lowlands and over population does not seem to have been a problem, you would expect the development of rice farming to have taken place first in areas that a submerged now. What we see in the Korat Plateau seems to support this as the development was sudden (although much archaeology remains to be done as there has been for less there than in the Mid-East)