Upcoming stopover at Hong Kong what to do about the protests?

Small but very important correction: what you have is a layover not a stopover. As such, you could spend the entire time airside ie past security. Unless they shut down the entire airport (which did happen before but not often) your flight will happen just fine, protests don't (can't) extend past security. I wouldn't worry too much.

Mid-September, I flew Germany to Japan with Cathay Pacific, also with a layover in Hong Kong. (I had to book literally the night before and for some reason Cathay Pacific options were the cheapest. You wonder.)

My layover was just over an hour (not short enough for them to permit me using the fast lane at security) but my entire experience at Hong Kong Airport was smooth. I believe that for most of the time during which there were protests this was the case, mostly because the airport is not that close to the inner city where most of the demonstrations are happening. Depending on the day of the week and the time (I arrived and departed early morning on a Monday) the chances of protests happening anywhere in the city could be close to zero.

I recall at least one time (but most likely two or three times) when Hong Kong airport was closed due to protests, so your risk is not zero. If it does happen, you may fall victim to force majeure clauses in the terms of service, but maybe CX will be able to arrange alternate arrangements for you to get to India without passing Hong Kong.

Tl;dr, your three main questions:

• Yes, layovers in Hong Kong are safe over 99 % of the time even during protests
• This depends on you but I wouldn’t
• They may claim force majeure (i.e. no refunds), their terms of service should certainly allow them to do so in the unlikely event that the airport is closed. They may be able to provide alternative arrangements.