Almost all U.S. LTL carriers use NMFC freight classes, although some are attempting to move to a dimensionally-based system.
No. If you claim that your freight is a lower class than it actually is, your carrier will likely find out. They will charge you a fee for reclassifying the freight and charge you the appropriate amount for the actual class of your freight after it has been shipped.
NOI stands for Not Otherwise Indicated. This is used when a commodity does not have an NMFC code. In these cases, density is usually used to determine freight class.