Is or can MG καθόλου be used as a noun in this context?
In this context (as Aristotle's one), no, it is'nt and it can't be used in MG.
If I understand correctly, MG uses καθόλου as an adjective but not as a noun (“το καθόλου”)?
Καθόλου as a noun in MG is rather rarely used, in the meaning of τίποτε (Notice the article το in front of καθόλου, turning it into a noun), e.g. Aπό το λίγο ως
το καθόλου υπάρχει διαφορά=From "little" to "nothing" there is a difference.
Is there another word used for English “universal” – as a philosophical principle that applies universally or common property found in a class of particulars, etc., “καθολικός όρος” (French universel, German Universalie)?
Apart of καθολικός see παγκόσμιος, οικουμενικός, γενικός. Even ολοκληρωτικός, συλλογικός, συνολικός with usage depending, of course, on the context used.
And can something like *καθέκαστον (< AG καθ' ἕκαστον) be used for the opposite (“particular”)?
MG: In MG there is no such word (in singular, although you might encounter it in an isolated monograph), but there is the word
τα καθέκαστα [< med. τὰ καθ΄ ἕκαστα] in the meaning: details, particulars of a case or an event. Example: Μάς περιέγραψε το περιστατικό με (όλα) τα καθέκαστα=He described the event in every detail.
If you're looking for an opposite of καθολικός in MG, see ειδικός, μερικός, επιμέρους.
AG:
τὸ/τὰ καθ᾽ἕκαστον,
τὸ/τὰ κατὰ μέρος και
τὸ/τὰ/οἱ ἐπὶ μέρους are opposites of καθόλου.
It isn’t entirely clear whether the word here is an adjective or a noun but it does seem to have a substantival function.
I could agree with you on that it does seem to have a substantival function as I think that the sentence "ἡ μὲν γὰρ ποίησις μᾶλλον τὰ καθόλου (τὰ κ. = universal truths), ἡ δ᾽ ἱστορία τὰ καθ᾽ ἕκαστον λέγει" advocates for that (Aristot. Poet. 1451b).