Why pushing a wall that is of a great mass does not move it? If I pushed a wall of a great mass that is connected to the Earth with a normal human force, it does not move, why? Is it the normal force that prevents it from moving? or does the Earth exerts a force on the wall that is equal in magnitude and opposite in direction to it?
 A: It does move—unless you're rigidly connected to it. 
If you're on a free-floating boat in a harbor and you push against the seawall, for example, then you (plus the boat) and the seawall will move apart. Of course, it will look like you're moving the boat rather than the seawall because the seawall is rigidly connected to the Earth, which has much more mass than you and the boat. Nevertheless, both you (plus the boat) and the seawall (plus the Earth) are moving away from your common center of mass.
If you're rigidly connected to the wall (including if your feet are braced by friction against a floor that's rigidly connected to the wall), then the mechanical connection prevents any relative movement. In this case, any pushing just adds elastic strain energy to the materials connecting you.
A: To understand what's going on, let us take a different example where a stick is glued to a box. To move the stick you would have to also move the box or break the adhesive force of the glue. Similarly to move the wall yoh would have to also move the earth or break the bond between the earth and wall.
Here I think you could say that the earth applies a force which negates the human force but I wouldn't call it a normal force. 
