This is so true. The original Persian culture is best preserved in India among the dwindling Parsi community. These are the original Persians who escaped to Gujarat, India during the Islamic colonization of Persia.
This isn't true at all. For hundreds of years, Parsis were almost purely culturally Gujarati. Also there's limited evidence that they "escaped", Zoroastrianism still had a large presence in Fars for a while after the Muslim conquest, and they were going to some of the largest mercantile ports in the world. Also there were lots of muslims that came from Iran to these ports as well.