Someone from Israel is called an "Israeli".
"Israel" is a proper noun. If you want to use it as an adjective, you use the word "Israeli", as in:Can you do any Israeli dances?
Yes. It's also a proper adjective.Yes. It's also a proper adjective.
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.
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 George is Georgian.
Mayan is itself a proper adjective.
The proper adjective for Siam is Siamese.
The proper adjective for Georgia is Georgian.