Since I'm not satisfied with the answers and it seems that people still stumble upon this question googling, I'll try to answer it.
First we need to understand what are some basic assumptions of the classical electrodynamics. As every other field in science it uses models to describe the nature. Some well known models are point mass, point charge, continuum etc.
Electrodynamics uses charge continuum and point charge models to describe charges in the real world. Charge continuum is given by one main quantity and that is charge density.
Charge density in a point $A$ is defined using averaging of all charges in a small volume of space $\Delta V$ around the point $A$. Also we average the charge density over some small time interval $\Delta t$. Now I will not go into details of what $\Delta V$ and $\Delta t$ actually are, but you can read about physically infinitesimal volumes and time intervals. The point is that $\rho(A)$ is not the "exact" charge density at that point, but rather the averaged value.
Now back to the question:
We know that conductors (metallic) have free electrons which randomly moves in all directions, so how come we can talk about electrostatics which by definition means stationary charges?
Yes, they do randomly move in all directions and that is the point. When you average out over small space and time intervals (given that electrons usually don't cross a long distance and don't have a great velocity) - you will get zero charge density. The key is the randomness of thermal motion which averages to zero. In jargon you would say that classical electrodynamics doesn't see the quantum and thermal effects because of its zoomed out scale.
That is perfectly understood, but my problem is the following: the original claim was that the electric field within a conductor is 0, not the electric field after putting the conductor in an external electric field it became zero. I do not understand the logic!
This second question is essentially already answered above. The authors usually assume trivial the question about field inside the conductor with external field $E_{ext}=0$, so they jump right away to $E_{ext}\not=0$