Minnesota is neither an adjective phrase nor an adverb phrase. Minnesota is a noun, more specifically a proper noun, a single word. A phrase is a group of words.
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.
The proper adjective for Siam is Siamese.
Mayan is itself a proper adjective.
Freudian is the proper adjective for Freud.
The proper adjective for Georgia is Georgian.
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.
"From Minnesota" is an adjective phrase because it describes the noun it is referring to.