The short answer is no. The adjective does not change the syntax.
The long answer is that nouns can convert class from mass to count or vice versa. There's an old joke that if you have a really powerful machine that turns anything into powder ("a universal grinder") then you can make any noun from a count noun into a mass noun -- "that's a lot of man on the floor."
To go the other way, you don't even really need a machine -- whenever you are comparing multiple instances of a mass noun, you convert it to a count noun: "the sands of Texas are whiter than the sands of Florida."
As a result, you will find many instances of nouns that are usually mass nouns being converted to count nouns.
For your examples, I find "a soothing music" hard to parse, "a deadly pollution" makes sense (we are imagining several instances of pollution, this one a deadly one), "a hot tea" is fine (with food items that are mass nouns, we convert them a lot when we are ordering them at a restaurant, e.g. I'll have a tea), "a hard work" sounds terrible to me when describing the mass noun "work" (which means labor) but there is also a count noun "work" (a creation arising from a lot of labor, like the works of Beethoven) and here it makes sense to describe one as "hard."
But the point is that the adjective has nothing to do with it. It's just that the mass noun has been converted to count, and there happens to be an adjective.
Frequencies
A search of COCA reveals the following frequencies, out of 3,303:
- make/makes/made/making a mistake 3087
- commit/committed a mistake 8
- make/made a blunder 9
- committed/committing a blunder 3
- do/did/does a blunder 0
These don't add up to 3,303 because I've excluded irrelevant collocations
Very clearly, making a mistake is the unmarked form.
I'm afraid that do a mistake/blunder is not attested in the data. In fact, having searched the British National Corpus, the Corpus of Historical American English, and the Corpus of Global Web-Based English, I cannot find a single attestation of I did a mistake/blunder (or any other forms of did, in any tense, person or number).
From this, I'm going to assert that do a mistake/blunder is not well-formed, grammatical, or even used in Standard British or American English. As I don't currently have access to corpora for other variants of English, I can't comment on their usage/currency.
Now, to the differences in meaning.
Definitions
commit
to perform (a crime, error, etc); do; perpetrate
make
to cause to exist, bring about, or produce
So, what are the implications?
commit vs make
Well, firstly, it should be noted that the parentheticals - a crime, error, etc are from the original, and the definition of perpetrate contains parenthetical deception, crime.
Now, while obviously not conclusive, lexicographers tend to put these terms as examples, generally taken from common uses. These are likely to be frequent collocates of commit and perpetrate.
This gives commit a distinctly negative connotation - you don't commit an act of charity, and even though that is perfectly well-formed, using it in that way infuses the act of charity with negative entailments.
Bottom line
Use commit when the act is immoral, illegal, or you wish to imbibe that sense. Use make for more neutrality. Do not use do in situations where native American or British English is expected.
Best Answer
Idiomatically, if we are referring to the spoon made of gold with the emphasis on it being a high quality gold spoon, and not just a gold-colored spoon, we call it a "gold spoon". Similarly, when a buyer is interested in buying something made of gold, they want a gold spoon, a gold ring, a gold necklace, a gold watch, etc.
Note that "gold" is both a noun (the substance/element gold) and an adjective (the color gold). Nouns can "act like an adjective" to modify another noun; this is called a noun adjunct. So a "gold necklace" is "a necklace of gold (the metal)", and a "gold spoon" is a "spoon made of gold". See also attributive nouns.
But "gold" can also be an adjective for the color of gold! So how does one know if your "gold spoon" is a NOUN-spoon containing the element Au (gold) or just happens to be an ADJECTIVE-spoon, like a plastic gold spoon from a box of gold-colored utensils? That has to be resolved by context.
Golden is an adjective describing the color gold (golden hair), made of gold (a golden crown), or metaphorical qualities of gold, such as success or prosperity as in "golden opportunities" (See google definition). While gold can be used for similar connotations, golden is more deeply connected to its metaphorical connotations, and is used to "sound fancy" or metaphorical as above.
One might describe eating at a fancy feast "using a golden spoon encrusted with diamonds", which very well may be gold-plated or better. In this case, referring to it as a "gold spoon" would sound too objective and plain.