Electric field near a conducting surface

Consider the electric field in a small region near the surface of a conductor in electrostatic equilibrium. The electric field in this region has only a normal component to the surface. Otherwise the tangential component would accelerate the free charges in disagreement of the initial hypothesis of equilibrium.

Since we are interested in the field near the surface we use a small Gaussian surface. if we choose a small cylinder, it is easy to compute the flux. There is only flux across the top of the cylinder. After getting the result we are only able to infer the value of the electric field in that small region. If we were allowed to extend the Gaussian to arbitrary large regions, the result for the electric field would be extended as well. But in the example of an arbitrary shaped conductor, we cannot consider a large Gaussian surface. The field would cross the Gaussian surface in complicated ways that we would not be able to compute the flux.

Well, you would draw a cylindrical Gaussian surface for a straight conducting line (or cylinder) of linear density $lambda = Q/L$.
If it is an infinite line, then you take a small patch because of the symmetry of the problem.
[Of course, it if weren't infinite you would have boundary problems at the ends of the conductor but that is Classical Electrodynamics problem.]
Furthermore you know that the field inside the conductor is 0 at equilibrium and that the electric field is always normal to the surface because if it weren't, charges would be compelled to move and you would no longer have an electrostatics problem.
Summa summarum, you need not take the whole conductor because of the symmetry and the fact that only on the outside you will have an electric field $neq0$

EDIT 1:
You can neglect the other charges because the Gauss law will be the same for them. If you have a mutated potato conductor, it doesn't matter what the charge distribution is. You know that in an electrostatic problem, charge will distribute itself on the surface in such a way that in equilibrium there is no movement (hence statics). Therefore, no matter which portion you chose, Gauss's law will be the same.

Gauss law is the simplest way of handling when it comes to charges and field flux. As I have said, if you have a potato conductor, it makes no sense to choose the whole Gaussian surface as one small patch is enough to calculate the field because you know that the charges redistribute along the surface so that $E_{inside}≠0$ . It would be impossible to integrate the whole potato.