Can I see/export the total field mapping in use?
Good question. I am sure in the 'old days' you used to be able to work you way back to such a list via the breadcrumbs, or maybe i am confusing it with Option Groups. But i just gave it a go and couldn't find a way to it.

Your best bet is to jump in to the DB if you have access and grab a copy of the civicrm_custom_field table, plus the civicrm_custom_group table