All your examples are correct. These are adverbs rather than adjectives. Specifically, they're participial adjectives that have been turned into adverbs using the "ly" suffix. They also all follow a pattern where the noun added to turn them into a compound is the noun that would be the direct object of the verb. (e.g., soul-crushingly bad = bad enough to crush souls). There are other examples that follow the same pattern (e.g., "breathtakingly beautiful").
The "add -ly and use it as an adverb of manner" construction doesn't seem to work on all compound participial adjectives. There's no such adverb as "hard-workingly" or "time-consumingly," for example, even though time-consumingly fits the same pattern as soul-crushingly).
Searching Google Books, I find only 25 results for "helping-adverb" and eight for "helping-adjective," so I'm not sure if they were so much abandoned, as such, but, rather, never very common to begin with.
"Adverb of degree" receives 5,500 Google Books results (major contrast with the above), so I would certainly say that one would be better off, in terms of likelihood of being understood, if one used that term rather than the one with "helping."
In terms of "credibility," I don't see anything particularly wrong, per se, with the use of "helping-adverb"—just a lack of currency. "Helping adjective," seems wrong, however, as English adverbs are defined in any current dictionary or textbook as modifying either verbs or adjectives, and hence "helping adjective" seems to make little sense because all cited examples would normally be classified as adverbs or adverbial phrases.
The idea of a "helper" word is, however, used in grammar sometimes; the Chicago Manual of Style, for instance, mentions "helper verbs." However, since all the examples cited above do pertain to degree, one could argue that "adverbs of degree" is more readily intelligible.
I don't think any term directly translatable as "helping-adjective" is commonly used in describing Japanese grammar, but Japanese is an agglutinative language, meaning that multiple word-like entities are frequently combined together to form what could be considered single words but that do the work of what could be a whole clause in other languages. To wit, Ikaserarezu..., whose basis is the verb iku "to go," could mean, in context, something like "Without anyone forcing him to go..." The various things added to the end of verb stems and then onto one another in turn are usually called in English-language descriptions of Japanese grammar "auxiliary verbs" or "helper verbs."
The rub: some of these "verbs" are conjugated as though they were adjectives: -yasui, as in yomiyasui "easy to read" (from yomu, "to read"), is exactly conjugated like, and functions as, an adjective. In fact, yasui exists on its own as an adjective in its own right, etymologically related though with a slightly different meaning. Hence, one might (though typically doesn't) speak of "helping-adjectives" in Japanese, and these do not necessarily have anything to do with degree.
Korean and Turkish are other agglutinative languages, so somebody familiar with them might have more to add on your last question.
Best Answer
No. Advice that was "wholesome in superlative degree" would be "very wholesome advice"; "much wholesome advice" means "a great quantity of wholesome advice". The word "much" modifies the noun "advice" (or maybe the noun phrase "wholesome advice"). Similarly, the word "any" modifies the noun phrase "other metal".
Both "any" and "much" are adjectives of quantity. They modify nouns; both can modify comparative adjectives (as in "much heavier", "any heavier"), and "much" can modify verb participles when they're acting as adjectives (as in a "much used frying pan") but they do not modify regular adjectives.