Does the neutron star collapse from the surface to the center or from the center to the surface? I think the collapse begins at the surface because in this place the gravity is always more intense than in the center. That's right?
 A: I am not clear about your question - it is either about the formation of a neutron star or perhaps about the collapse of a neutron star after it has formed.
If it it the latter, then the instabilities that lead to the collapse of a neutron star would begin near the centre of the star at the highest densities. Since the density of a neutron star is much higher in the interior than at the surface then the assertion in your question about where gravity is strongest is untrue.
If the density scales as $r^{-a}$, where $a$ is a positive number, then the mass inside a radius $r$ is given by (ignoring GR for a moment)
$$M(<r) \propto \int r^{2-a}\ dr \propto \frac{r^{3-a}}{3-a}$$
The gravitational  force at radius $r$ (again ignoring GR) is
$$g(r) \propto \frac{M(<r)}{r^2} \propto \frac{r^{1-a}}{3-a}$$
Thus if $a>1$, then the gravity increases with decreasing radius, and this is certainly the case inside a neutron star. The effects of GR only increase this central concentration effect.
Collapse timescales go as the free-fall timescale, which is $\propto (G\rho)^{-1/2}$ where $\rho$ is the density. Thus dense regions collapse quicker and the collapse would proceed on an inside-out basis.
The formation of a neutron star occurs during "core-collapse" and this terminology alone I think would answer your question in this case.
Just prior to core-collapse, the neutron star progenitor is a massive star with an iron core, of a bit more than a solar mass, surrounded by further shells of nuclear-burning material (silicon, neon, magnesium, oxygen etc) and then a large envelope of hydrogen and helium.
The collapse is triggered by instability in the core. Any contraction of the core raises it's temperature; the iron photodisintegrates; protons capture electrons to form neutrons; and since the electrons provided the principle support for the core via electron degeneracy pressure, then that pressure disappears. As a result, the core collapses very rapidly, basically according to the "free-fall time" of the material.
The free-fall time is roughly equal to $(G\rho)^{-1/2}$, where $\rho$ is the density. So the dense centre collapses even faster than the outer parts of the core. It is an inside-out collapse. The whole core collapse takes less than a second, before the rest of the star has any clue about what's going on. Eventually, on longer timescales associated with the sound speed, the outer parts of the star also start to collapse inward. Some of this material may get incorporated into the final neutron star, but much of it will be blown away by the supernova explosion that results from the core-collapse.
A: The reason giant stars don't collapse immediately is because they're supported by outflowing heat produced by nuclear fusion. When they run out of fuel, they lose this support and collapse until they can be supported by degeneracy pressure. So you could say the collapse starts from the inside in the sense that that's where the power former power source was before turning off.
A: increasing pressure at the center of a neutron star might trigger a phase transition to new state with higher density and while matter settles down the warping of space time might reach some critical value creating the full fledged event horizon at some radius below the surface of the neutron star.
this is all speculative, because very little is known about interior of neutron star and what densities matter reaches, there are ongoing astronomical observations tat might shed light on the problem
another possibility is that accretting mass build up would lead to the formation of the event horizon directly at the surface of the neutron star as you guessed, if there is no matter state with higher density to trigger the phase transition at the center of the neutron star
