Normal force - 3 things I don't understand So i have a couple of (lengthy) questions about the normal force.
Let's say i have a setup where a box falls from the air onto a rough surface, with a horizontal velocity. Let's neglect air resistance.


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*The very moment when the box hits the ground, wouldn't the normal force be larger for a brief period than the gravitational force? Of course, after this the forces would balance out but we have to get rid of the initial vertical velocity for it to slide on the ground and not fall in the ground right?

*When the box starts sliding, there is some dynamic fricion on the box dependent on the magnitude of the normal force from the ground onto the box ("due" to the gravitational force from the box onto the ground). But why is this the case if the normal force and the gravitational force are cancelled out? I mean, if they are cancelled out it shouldn't have any effect on the further path of the box right? (it is intuitive that the harder you press, the more friction you have but I don't see why because the normal force cancels it out)

*http://www.physicsclassroom.com/class/energy/Lesson-2/Internal-vs-External-Forces 
Here it is said that the electromagnetic force is a conservative force. If i'm not mistaken and all collisions are due to electromagnetism between the atoms' electrons then how can a system ever lose energy?
 A: 
The very moment when the box hits the ground, wouldn't the normal force be larger for a brief period than the gravitational force?

Yes, for the duration of the collision between the box and the surface, the normal force (the force that the surface is exerting on the box) will be larger in magnitude of the gravitational force acting on the box. As you say in your question, once the collision is over (assuming no bouncing) the normal and gravitational forces will equalize. The average increase in normal force can be calculated if you know the duration of the collision.
For example, let's imagine a box with a mass $m = 1\text{kg}$ falling from a height $h = 1\text{m}$. We can calculate what the velocity of the box will be once when it starts its collision to be $4.43\frac{\text{m}}{\text{s}}\text{[downwards]}$. If we know that the collision takes $0.1\text{s}$, then we can calculate the average acceleration to be $44.3\frac{\text{m}}{\text{s}^2}\text{[upwards]}$, which tells us that the average normal force for the duration of the collision is $ma+mg=54.11\text{N [upwards]}$.

When the box starts sliding, there is some dynamic fricion on the box dependent on the magnitude of the normal force from the ground onto the box ("due" to the gravitational force from the box onto the ground). But why is this the case if the normal force and the gravitational force are cancelled out?

Remember that just because the the gravitational and normal forces cancel, doesn't mean that they have no effect, it just means that they produce no acceleration. When the box is resting on the surface, it is still being pulled into the surface by the gravitational force, but it cannot be accelerated downwards because the normal force it supporting it.

Here it is said that the electromagnetic force is a conservative force. If I'm not mistaken and all collisions are due to electromagnetism between the atoms' electrons then how can a system ever lose energy?

Firstly, Conservation of Energy tells us that energy is never lost during the collision, it is only converted to other forms (sound, light, heat, etc.). I suspect, however, that you are more interested in the change in kinetic energy during a collision. Kinetic energy is always lost during collisions in the real world, but there are some examples of collisions which approximate elastic collisions—collisions in which kinetic energy is conserved.
Billiard balls are probably the most used example of an 'elastic collision' because they are made to collide with very little loss. You can clearly visualize the difference between colliding two billiard balls and colliding two sponge balls colliding—the sponge balls will not bounce off of each other very nicely.
The collision of the two sponge balls is an example of an inelastic collision, in which kinetic energy is not conserved. You can even detect the energy conversion yourself... Smack your hands together: you can hear the produced sound energy, and you might even feel the thermal energy.
A: Answer to the two first questions

The very moment when the box hits the ground, wouldn't the normal force be larger for a brief period than the gravitational force?

Yes, indeed. Newton's second law. For the box to stop and not break through the surface, the surface must exert a normal force large enough to not only hold back against the weight but also to slow down the box. It must also cause an acceleration. So it must be larger.

But why is this the case if the normal force and the gravitational force are cancelled out?

It doesn't have to cancel out. If you press a box onto the wall, then a horizontal normal force is exerted. The friction prevents it from sliding. The fact that the normal force cancels out  something something else is irrelevant. Friction is present when the rough surfaces are squeezed together - the size of the normal force is just as "measure" of that, do to speak. 
