As far as I understand, among the constructions
- (て-form verb),
- (て-form verb)いる,
- (finite verb)こと,
- (finite verb)の,
- (verb phrase)と,
- (finite verb)もの
the form (2) unambiguously functions as a finite verb (denotes a progressive, a perfective or an intention, can accept arguments like a normal verb), (3) and (4) unambiguously function as nouns (verbal nouns with subtly different meanings, can accept arguments as a normal verb).
My question is about the remaining ones: (1), (5), and (6). Basically, what are they, from a language-neutral perspective? From the outside, do they look like adjectives (participle? although seemingly any finite Japanese verb can qualify a noun as is), adverbs (transgressive), nouns (verbal noun), special non-finite verb forms of some sort (if so, what do they express?). Or should I just give up and say they only make sense as a part of set constructions?
The て form (1) seems to accept arguments like a normal verb and participates in a dizzying variety of constructions [～ても concessive, ～て下さる polite, ～ている progressive, chaining as in VPてVPてVP(finite), ...]. In some of them it can be replaced by a noun (concessive) or a noun with an を marker (polite), in some it can’t (progressive), in some it’s so special I’ve half a mind to mentally classify it as a different て altogether (chaining).
The と construction (5) I’ve seen used as a topic (～とは ...) or as a kind-of-object but without the accusative marker を (～と言う, for example, both as an action and qualifying something). It seems like the qualifying ～と言う (“so-called” as in ～と言うもの) can also be formed from a noun or just about anything, but I’m not sure about any other uses.
The もの construction (6) I’ve seen only as a topic (～ものは ...), sort of noun-like, but not really, as it doesn’t seem to be possible to use it as a noun anywhere else. The usage in ～と言うもの seems to suggest that it’s just a noun with a passive meaning: “something that is called ...”, but that’s only how I translate it for myself.
(As to mentioning the gerund in the title, seems like almost any one of these forms is called a gerund in one place or another—possibly because the -ing form in English can look as an adjective, an adverb or a noun from the outside.)