How does the mapping of the Feeds module work? Does the mapping of the tables from source to destination should be completed, if I have 6 fields in the source table? Should I list all 6 fields, or can I only put 1 field to map if I only want that field to be imported?
You can import as few or as many source fields as you want.  You do not have to include all of them!  The source table or cvs row or whatever does not have to match your destination entity exactly.  It's OK to just take the parts you need.  I frequently use the feeds module with csv files, and import just a portion of the columns that are actually present in the file.

Naturally, just make sure none of those missing fields are marked as required on the destination entity...