Answer by Balaji Viswanathan:
Do nothing. India is not for any splitting of China and again HK protestors are not asking for independence.
India has historically maintained a non-interference in the domestic matters of other countries. It is a matter of public policy. Almost all sovereign nations are quite capable of taking care of their own home.
Hong Kong's case is one of protestors asking for more rights in their domestic matters. There is a real estate mafia and people want a better management of this. China is big enough to tackle this.
Even assuming that China is weak enough to allow others and India wants to interfere, it is practically impossible to impose democracy from outside. Democracy has to have a strong domestic support.
In short, India is not likely to do anything. India's current Prime Minister understands that fixing the domestic issues is way more important than poking nose into neighbor's issues.