Can we stop an electron? In some scientific movies I saw that when they want to demonstrate the double slit experiment they compare marbles (in not quantum world) to electron (in quantum world) because both of them have mass and they say the only difference between these two are their size.
My question is: Can we stop an electron and put it on a surface as we can do to a marble, Or is movement the nature of electron and it can not be motionless?
 A: No, we cannot. A marble is a classical object which obeys Newtonian mechanics. The electron is a quantum mechanical entity, and that is what the double slit experiment demonstrates.
In quantum mechanics there exists the Heisenberg uncertainty principle (HUP)
$$\sigma_x\sigma_p\geq \frac{\hbar}{2}.$$
The uncertainty in the position times the uncertainty in the momentum have to be larger than $\frac{\hbar}{2}$. If the electron were still, the momentum would be zero and thus the location of the electron in space would not be defined. The HUP leads to an uncertainty in position or momentum or both. The functional behavior of the electron depends on the solution of specific quantum mechanical equations which will finally give a probability distribution for finding the electron at an (x,y,z) at time t if a measurement is performed.
In the double slit experiment with electrons one observes on the screen this probability distribution experimentally, i.e. nature solves the problem "double slit of specific dimensions impacted by electron of specific momentum".
The marble , although composed out of quantum mechanical entities, has about 10^23 of them ( Avogadro's number) , and the marble's dimensions are so large that the HUP is always true. Though the underlying nature of everything is quantum mechanical, macroscopic objects emerge from the large numbers of the underlying atoms obeyin newtonian mechanics because of this difference in the dimensions .
A: Whatever movie you saw was a gross simplification.  An electron is not a 'thing' in the classic sense.  We have no idea what it is, but the closest we've come to describing it is that it's a packet of probabilities that moves through space.  One popular visualization is that space is like a field of springs.  There's nothing actually moving through the field except a wave of potential as the spring at each point in space momentarily rises above it's ground potential, and then returns to it's ground state. Think of a 'wave' at a football stadium.  No one ever actually moves from their seat, but by each person standing up and down the wave can go round, and round the stadium.
And, yes, we've been able to freeze things to the point they don't move any more.  In this state the electron would form what's known as a Einstein-Bose condensate.  At this point the electron (we haven't actually frozen an electron yet, but the idea is the same) becomes spread out in space like a pancake.
Here's a pretty cool video of the process on the Wiki page.
