The efficiency certification ( 80 Plus, 80 Plus Bronze, Silver, Gold, and Platinum ) basically refer to how efficient the power supply can run at at a certain load, or what is its maximum efficiency. The best would be 80 Plus Platinum, while Gold comes in second. You can identify their ranking easily just based on the naming convention.

Efficiency also indirectly indicate the quality of the components used in the power supply that was awarded the efficiency certification ( Bronze, Silver or et cetera ) since to achieve a high efficiency you need to have good quality components.

That would be a yes, wouldn't it? It means less energy is lost through conversion, therefore less power draw is required from the wall socket.

How much power can it actually deliver? You can find that out using a PSU load tester.

Anyway, efficiency actually has to do with the amount of power that will be loss through conversion of AC power to DC power. A 500W power supply with 80% efficiency will still output 500W of power if it's built to do so, but since it only has 80% of efficiency at best then it will need to draw 625W of AC power to produce 500W of DC power.