The Ref #, Supplier Code, and Customer fields on the Add screen are there for reference, but that information is not permanently tied to the inventory record. Once the inventory is in the system, it is assumed identical to the rest of the inventory for that item, and those fields are not tracked through additional Move or Remove transactions. The Add transactions on List > Transactions will continue showing the information that was entered if you need to go back and verify it at a later time.
The other four fields, Serial Number, Pallet, Lot, and Date Code, are all permanently tracked with the inventory record. If you need the system to track additional information for each inventory piece, you will need to make use of one of those fields. You can rename the fields as needed, but they retain the original properties. I.e., even if you rename it, Serial Number will always require a unique value.
These TrackBy fields can only be used if they are checked on the New or Edit Item screen. If you need to begin tracking one of these fields for an existing item, you will first need to remove any active quantity for that item, enable the field you wish to use, then re-add the quantity with the required field filled in.