How do you import (custom) relationship fields?
From what I can tell this functionality is not available in core imports, which allow relationships to be imported as a side function (e.g. when importing contacts, you can specify relationships on the side). 

There is an extension available called "CSV GUI Import to api" which allows more targeted imports, including one directly to Relationships. 



I think you need to use Internal Contact IDs (I tried to find how to do it with external IDs and couldn't manage it), as well as having other info specified:



In the screenshot above (from the second field matching step), "Year" is a custom field that I added to a certain relationship type, and which can be imported to in this way. You can see the core date fields are also available.