Sixteen distinct positive integers from 1 to 16 are placed in the cells of a 4x4 grid in a random order, with each number occurring in a cell exactly once.

Determine the probability that the absolute difference between an integer and any of its neighbors (including diagonally) is more than 2 but less than 13.

As a bonus, determine the probability that the absolute difference between an integer and any of its neighbors (including diagonally) is more than 2, but less than or equal to 16.