Can I buy health insurance policy if I am not an Indian National but am living in India?

Yes, if you are a student studying in India or working on a valid work Visa then you can get the policy. But if you are a tourist coming to India for 3 weeks, it will not be worthwhile to buy this as 30 days cooling off period itself offsets the benefits which you are looking for. Medical tourism cases are definitely not covered in policy issued in India.