With regard to the number of Stations it is not at all easy to determine how this came to be fixed at fourteen, for it seems to have varied considerably at different times and places.
The article as a whole actually goes into quite a few different variations which are found and expounds on those which were varied and altogether absent. To compound the matter further, some parishes will include a 15th station: the resurrection.
It is my suspicion (using this article), but this is, at best, speculation, that it happened to be that the 14 stations which are used today happen to be the 14 stations which were used at the time in Rome. It is not unheard of for normalization to be propagated based on what was common in the area of the Roman See and, lacking better evidence, this seems like it makes for a good fit. Of course the fact that there were a number of published documents describing things not wholly unlike the modern practice from the two centuries prior does not hurt either.
This ambiguity was also something which lead to Blessed Pope John Paul II creating a new stations of the cross in the 1990's.
While this is by no means a mystery on the level of the sacraments, it is still something which cannot be known.