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It is common knowledge that na-adjectives are in truth nouns that can be used
as adjectives (edit: I now see this was a false generalization I was led into
believing by some grammar sources); and the commonest formula where it's
obvious the na-adjective is _used as an adjective_ is "na-adjective+な+noun".
But when they are used as the predicate in noun sentences (i.e. **" na-
adjective+だ/です"**) I can never be sure if what is meant is a noun, or an
adjective.

For example, below are examples where a na-adjective is used as a predicate:

これは幸せです。-> Does this mean "This is happiness" OR "This is happy (this is a
happy occassion)

空はきれいです。-> Does this mean "The sky is beautiful" OR "The sky is beauty (the
sky is the definition of beauty)"?

夜は静かです。-> Does this mean "The night is silent" OR "The night is silence (in a
poetic sense)"

While in the above examples, the na-adjectives are _grammatically_ nouns; most
of the time in the English translation, they are adjectives. I'm assuming the
first translations I've given above would be the commonest choice of meaning.
However, in the case of 幸せ, what is meant is a noun; in the case of きれい and
静か, what is meant is an adjective. **How does one tell if a na-adjective used
as a predicate is meant to be an adjective and not a noun, or vice versa?**

Is it simply a matter of _how often_ they are used as nouns when used without
な? (i.e. do we translate 幸せです as "this is happinnes" as opposed to "this is
happy", simply because 幸せ is very often used as a noun?)
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adjectives nouns na-adjectives
How to tell when a na adjective is being used as a noun (as opposed to an adjective)
Some _-na_ adjectives can also be used validly and grammatically as nouns.
Your example sentences happen to include _-na_ adjectives that cannot be used
as nouns.

  * 綺麗【きれい】 is only ever an adjective. The noun form would be 綺麗さ. 
    * [Nihon Kokugo Dai Jiten (NKDJ) entry at Kotobank](https://kotobank.jp/word/%E7%B6%BA%E9%BA%97%E3%83%BB%E5%A5%87%E9%BA%97-247288) (in Japanese). Note that the part-of-speech marker at the top only has 『形動』 (short for 形容動詞【けいようどうし】 or " _-na_ adjective").
    * [Digital Daijisen (DDJS) entry at Kotobank](https://kotobank.jp/word/%E7%B6%BA%E9%BA%97-480543) (in Japanese). Note the same part-of-speech marker. Note too the 『[派生]きれいさ［名］』 line towards the bottom, showing that the noun derivative is formed by adding ～さ on the end.
  * 静【しず】か, outside of extremely rare exceptions such as 「静かの海」 as noted by @[broccoli facemask](https://japanese.stackexchange.com/users/7810/) in the comments, is only ever an adjective. 
    * [NKDJ entry at Kotobank](https://kotobank.jp/word/%E9%9D%99%E3%81%8B%E3%83%BB%E9%96%91%E3%81%8B-282013) -- this one includes the noun derivative towards the bottom of the page.
    * [DDJS entry at Kotobank](https://kotobank.jp/word/%E9%9D%99%E3%81%8B-519671)

In these cases, even when used predicatively, we know that these words can't
be nouns unless they include the nominalizing suffix ～さ, so constructions like
「あの子は綺麗です」 or 「この森は静かです」 can only be understood as `[NOUN = ADJ]` sentences.

In those cases where a _-na_ adjective can also be used as a noun, such as
幸【しあわ】せ, context can help you figure out the intended sense.

  * 幸【しあわ】せ 
    * [NKDJ entry at Kotobank](https://kotobank.jp/word/%E4%BB%95%E5%90%88%E3%83%BB%E5%B9%B8-2044698), showing a part of speech of 〘名〙, but then also including examples with clear _-na_ adjective constructions.
    * [DDJS entry at Kotobank](https://kotobank.jp/word/%E5%B9%B8%E3%81%9B-515403), showing a part of speech of ［名・形動］.

Your sample sentence:

  * これは幸せです。 
    * We don't have a lot of context here. That said, it's not that common that people talk about something being "happiness itself", so this is most likely saying that これ is 幸【しあわ】せ as an adjective: _" happy, fortunate, lucky"_.

⇒ Beware of the pitfalls of translation, however! While it may be valid to
parse this sample sentence as `[THIS = NOUN]`, we have to think about how
Japanese fits together conceptually. Considering the senses of 幸【しあわ】せ, in
terms of _" things coming together in a favorable way"_, even were we to use
the noun interpretation, it's probably a better translation to think of this
as _" an **instance** of things coming together in a favorable way"_, rather
than any kind of over-arching meaning of _" the essence of favorable
coincidence in any and all circumstances"_.

Looping back to your core question:

### How does one tell if a na-adjective used as a predicate is meant to be an
adjective and not a noun, or vice versa?

  1. Check the dictionary for the part of speech for the word. 
    * Not all _-na_ adjectives can be used as nouns.
  2. Check the dictionary for details on the meaning. 
    * If the word can be used as a noun, does the noun make sense in your context?
  3. Check usage patterns. 
    * Does the meaning you're thinking of still work when the term is used in other sentences? Google, Linguee, and other search engines can be your friend in this regard.
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