Consider the neutral, Schwarzschild black holes in $d=4$. If they're large, they're solutions to Einstein's equations. However, Einstein's equations have higher-derivative correction terms that go like $(L^2 R)^k R$ where $L$ is a characteristic length and $R$ is the Riemann curvature, schematically: many possible contractions are possible.
These terms may only be neglected if $L^2 R\ll 1$ i.e. if the characteristic size (curvature radius) of the black hole is much greater than the coefficient $L$. Because the coefficient $L$ in the effective action (governing the higher-derivative terms) is of order the Planck length, the higher-derivative terms may only be neglected for black holes much larger than the Planck length.
At least parameterically (up to numerical constants of order one), it's the same condition as having the mass much greater than the Planck mass, too. Also, black holes obeying such an inequality have the lifetime (of Hawking evaporation) that is much longer than the Planck time, too.
It makes no sense to consider black holes that are smaller than the Planck length because the solutions to Einstein's equations aren't relevant: one should consider the solutions to the equations including all the higher-derivative corrections. The nature of geometry changes dramatically below the Planck scale. Also, black holes that are smaller than the Planck length have the evaporation lifetime shorter than the time needed for light to get from one side of the hole to the other. It makes no sense. Such an object is so unstable that it makes no sense to consider it.
In reality, the black holes are described by microstates that are discrete: there are only $\exp(A/4G)$ microstates for a given black hole. This quantization becomes important for very light black holes. The number of "black hole microstates" that are lighter than the Planck mass is actually finite: the microstates are the elementary particles we know. The approximation of Einstein's equations totally breaks down. Instead, these particles should be described as point-like perturbations on a pre-existing flat spacetime background.
When one tries to collide particles (e.g. protons) of ever greater energies, he may probe ever shorter distances. However, this process breaks down once the energy of the center-of-mass energy of the protons approaches the Planck mass (a universe-sized collider is needed). In the critical transition regime, one expects to probe distances of order the Planck length. However, one actually creates a black hole of the same radius. When the energy of the protons is increased beyond that, one no longer studies "ever shorter distances"; instead, one creates ever more massive i.e. ever larger black hole. You can see that the minimum distance one may really probe is comparable to the Planck length.
In various mathematical contexts, one may "consider" distances that are shorter than that. However, it's important that physics doesn't obey the naive laws of physics in an ordinary classical geometry, as we know it from long distances. The most general generalization has to be assumed to replace our usual framework of "objects on a pre-existing spacetime geometry".
On the other hand, one must realize that the new Planckian effects and restrictions only occur if some Lorentz-invariant distances become formally shorter than the Planck length. For example, the wavelength of a photon isn't Lorentz-invariant. That's why the wavelength may be arbitrarily short, arbitrarily shorter than the Planck length, too. That's guaranteed by the Lorentz contraction in special relativity. Only distances describing the internal structure of something as seen from the "rest frame" start to behave wildly once we reach the Planck length.
The information preservation is an entirely different and huge topic. Yes, in some sense, the information is preserved at the horizon. It returns when the black hole evaporates. For very small black holes, this description isn't too useful because we can't take the "location of the horizon" too seriously as the quantum corrections and fluctuations are very strong, as argued above.
