The National Motor Freight Traffic Association (NMFTA) publishes a list of freight class designations, codes, and subclasses for commonly shipped items (https://classit.nmfta.org/). A subscription is required to view this list. You can read more about freight classes at Koho for free on our freight classes pages.
Adding NMFC code to a shipment is technically optional, but the NMFC codes can help avoid reclassification and ensure you're using the correct freight class number.
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.