My answer should possibly satisfy you, I think. Here is an artist's conception of Mars Science Laboratory Entry, Descent & Landing...
Curiosity is large in size as it has 10 science instruments to find the availability of life in Mars. Also it uses Multi-Mission Radio-isotope Thermal Generator for fuel. Hence, airbags cannot be used to handle such a large weight since more fuel has to be supplied to carry them and also cannot be expected for such a soft touchdown. Even Aerobraking does not help the landing as @dmckee has already told about it. Moreover, three satellites such as European Space Agency's Mars Express Orbiter, NASA's Mars Reconnaissance Orbiter & Viking Orbiter were used to study the environment of Mars for the safe-landing of Curiosity. After the entry of the Rover into Mars' atmosphere, the processes such as Parachute deploy, Separation of Heat-shield, Radar data collection, Separation from the Aeroshell & using the rocket-powered boosters named Sky Crane and even touchdown are all handled by Curiosity. Hence, NASA mentioned this as seven minutes of terror.
The rocket-powered boosters is a new type of landing system which provides enough upthrust to overcome the gravity of Mars and the force exerted on the rover during entry. This is a proposed landing system because three orbiters are out there to update each situation.
But even after these precautions, the count-down of Curiosity landing was not appropriate as expected. The Rover landed some minutes later than the expected time due to severe problems in atmosphere during its entry.
And, I'm helpless to answer your 3rd question as others have already commented it. And yes, they're very true. Scientists have done millions of simulations and tests before taking such a risky landing system.