India was NEVER called “Sanatana-dharma” (see also the correct spelling) – “Sanatana-dharma” means “Eternal law” (eternal dharma, religion) – so it refers to Vedic and Brahmanic religion known today as Hinduism.

India was called “Jambu-dvipa” or “Bharata-varsha” (the modern name of India is exactly “Bharata” in Sanskrit, or “Bharat” in Hindi).

> The first Sutra says Yoga is open to all and there are no restrictions.

It doesn’t say so, nor anything close to it. It simply says: “Atha yoga-anushasanam”, which means “And now – the exposition of yoga [is being made]“. It is directed to the initiated students, as all the commentators underline, that the word “atha” (and now, here, behold) has the power of initiation.