The proper noun for the proper adjective Austrian is either Austria, the country, or Austrian, a person from Austria.
Vienna is a proper noun, the capital city of Austria. The proper adjective is Viennese.(The city name in German is Wien.)
A village is a small settlement, smaller than a town. Different parts of the world will have different ideas of how small a village is; generally a village in a densely populated area is bigger than one in a sparsely populated one.
The proper adjective for southwest is "southwestern."
The proper adjective is Haitian.
The proper adjective for Portuguese is "Portuguese."
Vietnamese is the proper adjective for Vietnam.
The proper adjective for Georgia is Georgian.
The proper adjective for George is Georgian.
Freudian is the proper adjective for Freud.
Mayan is itself a proper adjective.
The proper adjective for Siam is Siamese.