What are the definitions of elevator angle of attack and critical angle of attack?
Angle of Attack is the angle between the chord line of the airfoil and the relative wind. The elevator is also a "wing" in the effect that it is an airfoil.


  1) Then what is the angle between the chord line of the elevator and relative wind? Because if I am not wrong, by pitching the elevator up, the wing of an aircraft is subjected to the 'angle of attack'.


It's also called "Angle Of Attack". Pitching the elevator up also changes the angle of attack of the elevator. There are such conditions as elevator stall, although much less common than wing stall.


  2) When you say angle of attack exceed critical angle of attack, is it because the elevator is pitched up thus creating wider angle between the chord line and the relative direction of the wind?


The "Critical AoA" is the angle at which the airfoil is generating the most lift. 


  [Wikipedia Article on AoA]: The critical angle of attack is the angle of attack which produces maximum lift coefficient. This is also called the "stall angle of attack". Below the critical angle of attack, as the angle of attack increases, the coefficient of lift (Cl) increases. At the same time, above the critical angle of attack, as angle of attack increases, the air begins to flow less smoothly over the upper surface of the airfoil and begins to separate from the upper surface


Usually when you exceed the critical AoA, the air on the upper surface of the airfoil de-laminates and becomes turbulent. This results in a loss of lift (stall). 


Source: FlightSimBooks.com


  3)In the Air France 447 accident, the PF kept saying, keeps the wings level. What does it mean? How can the wings be leveled when the angle of attack is so high? Does keeping the wings level means reducing the angle of attack to zero?


I'm not sure what context you are talking about. I've read the transcripts pretty carefully and I don't recall the PF saying to keep the wings level. The Captain said to descend, while the PF was trying to climb. The SIC was pushing the stick forward while the PF was pulling back, causing the wings to remain level (or at a slight climb). 

Keeping the wings level (avoiding an un-coordinated turn) in a stall condition is the best way to avoid putting the aircraft into a spin. This is possibly what they meant, although they didn't know that they were in a stall (or if they did, they were not reacting to it appropriately).

Yes, leveling the wings would be making the AoA at zero (zero meaning where the airfoil is developing lift, and depending on the bank angle), but only if there were positive airspeed to make the relative wind parallel with the chord. In the case of AF447, the aircraft was falling out of the sky at a spectacular 15,000 FPM, which means that the relative wind to the airfoil was basically perpendicular. They didn't have the forward airspeed to change the AoA, so they should have lowered the nose to gain airspeed and decrease the AoA. 

The important thing to remember is that the pitch angle of the aircraft is not the same as the AoA. You can take an aircraft at zero forward speed and drop it straight down, the pitch angle will be zero but the AoA will be perpendicular.