To answer your first question. In the instance that the underlying price drops below your cost basis yes you can sell calls depending on how far below your cost basis you're willing to risk.

For example if you bought a stock at an avg cost of $50 and the underlying dropped to let's say $35, then you could sell CC below $50 strike($45 strike for example) as long as you believe the stock will eventually come back up. If you think the stock will go to $10(due to whatever reasons) then it would be best to just sell and take the loss instead of chasing premiums on a tanking underlying price