HSN stands for Harmonized System of Nomenclature. It is a system for classifying commodities created by the World Customs organization. U.S. LTL shipping, however, uses NMFC classifications instead.
Your freight cost is determined by a number of variables, such as how far your shipment needs to go, the freight class number, whether or not accessorials are needed, as well as fluctuating fuel costs and truck capacity.
No, not all commodities have freight subclasses, although many do.