A few things first to clear the air. (1) "Refined" can mean many things from simple filtration of foreign particles to a complicated process involving many steps, techniques, and chemicals. (2) The blog you link is not a reputable source, and neither are most "health food" sites that pop up when doing a search on this subject. As good skeptics, we want some measure of science, and even then we need to examine the evidence.
With that out of the way, let's just understand the basic bargain. Unrefined oil contains "impurities" some of them good for you, like nutrients or plant proteins, and some bad, like plant carcinogens or rat feces. Good and bad, these "adulterants" may taste bad, burn, or spoil easily. In general, unrefined oil will burn at a lower temperature and spoil faster than refined. Conversely, refined oil can withstand higher heat and will keep longer. That is the big picture here.
Now, to your questions.
Do oils become less nutritional after refining? A definite yes. The refining process removes iron, calcium, and magnesium among other things. Less harmful? That is a much more difficult question. This study, for example, finds that "epidemiologic investigations of lung cancer among Chinese women have implicated exposure to indoor air pollution from wok cooking, where the volatile emissions from unrefined cooking oils are mutagenic." In other words, if you are going to burn things over a fire, you better burn the pure stuff.
Why are refined oils popular in India, and elsewhere? In the words of Roy A. Carr in the Journal of the American Oil Chemists’ Society:
Crude vegetable oil contain variable amounts of non-glyceride impurities, such as free fatty acids, non fatty materials generally classified as "gums" or phosphatides, color pigments, moisture, and dirt. Most of these materials are detrimental to the finished product color, flavor, and smoking ability, and must be removed by purification step.
Are unrefined oils harmful in other ways? The answer is again, unclear. Unrefined oils by definition contain stuff that is unaccounted for, some bad and some good. Refining produces a uniform product with known and controlled contaminants (hence journals with appetizing titles like Oil and Soap).
Please note that this answer does not constitute medical advice. It is only meant to summarize published research related to the original claim and limited to the cited sources. Consult your physician about what these results may mean for your health.