Almost all U.S. LTL carriers use NMFC freight classes, although some are attempting to move to a dimensionally-based system.
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. While density is one of the primary factors in determining NMFC freight class, other factors, such as value, are also used in making that determination. Gold bars, for example, are very dense, but they fall into shipping class 500 along with very low-density items because of their high value.