The Indo-European language family, of which English, German, French, Spanish, Italian, Latin and Hindi are all members, originated someplace near, or in, present day Armenia. The tribes that spoke proto-Indo-European migrated from that point into Europe and India. It was the Aryan invasion of India (not really an invasion so much as a migration spanning hundreds of years) that brought the precursors of Hindi and of Hinduism to India. The language family in India prior to that was Dravidic and Dravidic languages are still spoken in south India.
The clockwise swastika is very popular in India. I just came from a three week trip there and you do see it very frequently. My in-laws have it on their door and elsewhere in their home, for example.