"Doctors" is not an adjective. It is a noun, and can be used as a verb. In common talk, it is a common noun: "He went to the doctor yesterday". In identifying a certain doctor, it is a proper noun: "Doctor Fleming will see you now". As a verb, it means to fix or tinker with: "By doctoring the recipe, he was able to give it more of an Italian flair."
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 George is Georgian.
Mayan is itself a proper adjective.
The proper adjective for Siam is Siamese.
The proper adjective for Georgia is Georgian.
Freudian is the proper adjective for Freud.
No, old is not a proper adjective. A proper adjective is an adjective derived from a proper noun, such as Swiss cheese, Bolivian pottery, Chinese silk, etc.
The proper adjective for Antigua is Antiganantigan
Kuwaiti is the proper adjective for Kuwait.