The first Mexican cancel is part of a duplex cancel, yes; the second may or may not be that. You might have noticed that some US duplexes look remarkably close to some Mexican ones; these were very likely manufactured by the same company.
The Spanish stamp does not have a barred numeral cancel. A barred numeral cancel is just that, a number or number/letter code for an office between bars. It is often the killer portion of a duplex cancel. They are also typically from an earlier period than the Spanish stamp shown.
The 1st cancel is an air mail cancel. Correos aeréo on top. Barcelona on the Bottom. Madrid example below. They exist from different towns.
___________________________________________________________________ You may want to take note that the main type of hexagone cancels are "Ambulante" types. They are either Train,Maritime,or Omnibus.They don't have the sides of the Hexagone like the airmail cancel,but they have 6 sides. A little link to these types: http://sanfilatelio.afinet.org/bibl...chadores.htm