No. The compound noun "Sunday school" refers to certain religious education, not merely school held on Sunday. In any event, the proper noun Sunday would be considered a noun adjunct, or attributive noun. In many cases, Sunday would be called an adjectival noun, because it is a form of the prepositional phrase "on Sunday" as in "We will go to church Sunday."
It is neither: it is a proper noun for a holiday.(In 'Easter Sunday' it is a noun adjunct with the proper noun Sunday.)
Sunday should be capitalized and school shouldn't be.
The possessive form Sunday's is an adjective. The word Sunday in "Sunday paper" is not an adjective but a noun adjunct, because Sunday is not a characteristic of paper.
Sunday is a proper noun
The proper adjective for Siam is Siamese.
It is neither: it is a proper noun for a holiday.(In 'Easter Sunday' it is a noun adjunct with the proper noun Sunday.)
Sunday should be capitalized and school shouldn't be.
The possessive form Sunday's is an adjective. The word Sunday in "Sunday paper" is not an adjective but a noun adjunct, because Sunday is not a characteristic of paper.
The proper adjective for Portuguese is "Portuguese."
The proper adjective for southwest is "southwestern."
The proper adjective for Haiti is Haitian.
Sunday is a proper noun
Vietnamese is the proper adjective for Vietnam.
The proper adjective for Siam is Siamese.
The proper adjective for Georgia is Georgian.
The proper adjective for Mayan is "Mayan."
The proper adjective for George is Georgian.