This is a difficult question to answer, because both aches and pains are subjective experiences - like colours - which you're unable to share, but assume everybody understands. I would have assumed that every language has words for both ache and pain, so a dictionary would tell you the difference in an instant. But, I would also assume you've done that, so your native language might not (I'm interested to find out what language that is).
An ache is a persistent discomfort, typically dull so that you can try to ignore it, but sometimes all-encompassing, yet not sharp enough to describe as pain. Your legs would ache after a tough run; you would not describe this as pain. You usually get a headache, not a head pain. You would suffer pain when you cut your finger, then experience an ache as the wound heals.
A pain is something more localised, often (but not always) short-lived, and something you'd be less able to ignore.
When you receive an injection, there is a pain as the needle goes in. During the following days, the surrounding area will ache.
There is considerable overlap between the two, and it would be quite acceptable to say "the ache in my shoulder is painful".
Poets and songwriters quite often speak of their heart aching. This fits well with a persistent sense of yearning or melancholy. If they said there was a pain in their heart, it would suggest a quite different emotion.
Describing pain and discomfort is difficult and subjective; I imagine in any language. When a doctor asks you how much something hurts, how can you explain in a reliable way?
This is nominalization produced by zero derivation. That happens when a non-noun is used as a noun without requiring that some derivational affix be applied to do so.
Per Wikipedia:
In linguistics, nominalization or nominalisation is the use of a word which is not a noun (e.g. a verb, an adjective or an adverb) as a noun, or as the head of a noun phrase, with or without morphological transformation.
[...]
Some languages simply allow verbs to be used as nouns without inflectional difference (conversion or zero derivation), while others require some form of morphological transformation. English has cases of both.
This in particular is zero derivation, which again per Wikipedia is:
In linguistics, conversion, also called zero derivation, is a kind of word formation; specifically, it is the creation of a word (of a new word class) from an existing word (of a different word class) without any change in form. For example, the noun green in golf (referring to a putting-green) is derived ultimately from the adjective green.
Conversions from adjectives to nouns and vice versa are both very common and unnotable in English; much more remarked upon is the creation of a verb by converting a noun or other word (e.g., the adjective clean becomes the verb to clean).
In other words, this happens constantly and is wholly unremarkable.
Best Answer
All are correct.
But are the compound nouns frequently used, or is the list frequently used?
If it's important to state 'frequently', here are some possible alternatives:
If the compound nouns are frequently used:
Here is a list of frequently used compound nouns.
Here is a list of compound nouns that are frequently used.
If the list is frequently used:
Here is a list of compound nouns, that is frequently used.
Here is a frequently used list of compound nouns. (this one still slightly ambiguous)