Is there a field type that allows a user to enter a value, and it builds a list of those values... and they can delete values. It'd be like a Dropdown field, or even Query Dropdown, but how would that tie in with a user-built list?
Nope. Sounds like a Tag fieldtype though, which is planned in a later release and will likely be an extension of the existing select fieldtypes. Added a feature ticket for this so we don't forget about it.
forge.joomlapolis.com/issues/7027
Or would this be two fields working together: use a text field for entry, Auto Actions to take that entry and populate a second Query Dropdown?
I suppose that's possible. You could move the value of the text field to a separate database table using CB Auto Actions and its Query action then query for those options using CB Query Field. Not sure how you'd go about removing entries though.