Using them as descriptors, can they be interchanged?
E.g. 親切な人 vs 親切の人
Is の only acceptable if referring to a specific new person from a certain place that has been established earlier in the conversation?
Using them as descriptors, can they be interchanged?
E.g. 親切な人 vs 親切の人
Is の only acceptable if referring to a specific new person from a certain place that has been established earlier in the conversation?
Both 新しいな車 and 新しいの車 are ungrammatical. 新しい is an い-adjective, and there is no interceding particle when い adjectives precede a noun.
な adjectives (e.g., 静か、変) require な when they precede a noun. 静かな部屋, not 静か部屋.
焔 is not an adjective; it's a noun. The particle の is used between nouns, even when a noun is being used in a descriptive sense. There's some overlap between な adjectives and nouns in Japanese, but in this case, 焔な扉 would definitely be incorrect. You can get a hint of how this sounds wrong by looking at how you translated the phrase: "door of flames". "Flames" is clearly a noun in this translation, as it is in the original. "Flames door" sounds odd to me in a similar way to 焔な扉.
You can definitely find song titles with な adjectives in them; I just searched my local karaoke box for songs with きれいな in the title and got plenty of results, such as Pizzicato Five's 君みたいにきれいな女の子.
Here's a lot more on Japanese adjectives from Tae Kim's guide.
I think you need to review the basics of Japanese adjectives. 新しい is an i-adjective, which means it requires neither な nor の. You always have to say 新しい車. Saying 新しいの車 or 新しいな車 is just plain wrong.
For na-adjectives, you always have to use な to directly modify a noun attributively. Using の instead is just plain wrong. As an exception, a few adjectives can take both な and の almost interchangeably, for example あいにく, but the number of such adjectives is smaller than you might think.
焔な扉 is just plain wrong because 焔 is not an adjective but a noun. の is a particle that links two nouns similarly to English "of" as in "door of flame". Some nouns are often referred to as no-adjectives because they are typically translated into English using adjectives. Anyway, you need memorize the word class of each word, and use な or の properly.