I agree that it's either a noun or an adjective.
I largely disagree with the usage note that mad cited in the thread that Möwe cited in #2 above. related discussion: Latino (weiblich) - #5
Perhaps it's just that I know Spanish, so I can't not notice feminine endings in words of Spanish derivation. But for whatever reason, I would definitely say that a woman is a Latina (Chicana, Filipina) novelist, with the correct ending.
I would guess that the feminine forms of these few Spanish words have become the default precisely because everyone and their dog (in the US) knows that much Spanish. You can't not know that feminine forms end in -a; it's just a very, very basic piece of knowledge.
However, there are other words that seem similar on the face of it but don't follow that pattern. 'Hispanic,' for instance, is invariable whether as a noun or an adjective.
And as far as I'm aware, nouns or adjectives linked to other languages than Spanish aren't similarly marked. A woman from Haiti, for example, is still a Haitian, not a Haitienne.
Again, I think that's basically just because Spanish is the foreign language most of us know best.