I am trying to do some research and I need to work with Demographic data for asian countries.
Where can I find such dataset/API. What are the limits to use each data in research ?
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if you want something comparable to the united states decennial census, then you want
Given the breadth of your question, there are probably a lot of other good resources which should be listed, but here are three of the big ones.
The Population Reference Bureau's DataFinder provides access to many data sets. From what I can tell, it would be a manual/interactive process to filter down to the data set you want and then download it as an Excel file. Also, it does not simplify the process of identifying only Asian countries among all represented countries. Nevertheless, there is a wide variety of data available. I didn't find any explicit data license, but by all appearances, the data is free to use.
UNData also provides access to a wide variety of statistics—the front page of the site says "34 databases—60 million records." It has an API, although based on SOAP and XML, which many developers find offputting.