な-adjectives are adjectives, despite functioning as nouns in almost all respects. Not entirely sure why some are mentioned in the dictionary as being nouns as well, because I sure ain’t never seen them actually functioning as a noun. That I can think of.
Noone’s ever really explained to me what “の-adjectives” are. Near as I can tell, they’re just nouns that are used to modify other nouns more often than not.
It’s useful to know which nouns often form する verbs, though. My dictionary mentions it – it’s got a little note saying [v-s] in the parts-of-speech field. Make a note of it if you like. =)