You must buy direct from the airlines to be eligible

if use credit card to pay for air ticket via travel agent, not entitle

Hard to say. I have a delayed luggage and the credit card's insurance paid me more (based on how much I can spend after how many hours) than the travel insurance (paid a fixed sum after how many hours).

Again hard to say. Different credit card have different condition. Some doesn't need it to buy air ticket and as long as you use your CC overseas, you are covered.

some card like some Standard Chartered's doesn't require you to use their CC to buy air ticket to qualify for their travel insurance. All you need to do is, once you landed in a foreign country, use the card once and you are covered.