Can an Indian national residing in Kuwait apply for a Schengen visa from India?
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Your are usually required to apply at the consulate or embassy for your place of residence. There are exceptions, but you should not start your application by explaining why you are a special case if you can avoid that.
You are not required to travel directly from your country of residence (or from your country of citizenship).
You are required to give an itinerary in your visa application, and you are required to broadly follow your itinerary. You can make minor adjustments, but your trip should be recognizably the one you applied for. (For multi-entry visas, that applies to the first trip.)