The titular use developed later than the OT (particularly in the Enochic tradition), but the generic use persisted as well. Both were available for Jesus to draw on and most scholars do recognize that Jesus as represented in the gospels used the expression "son of man" in different shaded ways. The apocalyptic "son of man" sayings represent a special group that is shaped by eschatological judge figure in Daniel 7 and in the Book of Parables, a usage that ultimately is derivable from the generic but which developed on its own trajectory. The non-apocalyptic uses of the expression in the gospels that reference Jesus' suffering, death, and resurrection, on the other hand, do not derive from this apocalyptic trajectory. They instead are a new special use of the generic "human being" deployed circumlocutionarily in self-reference to highlight his own human mortality. The question then is, if Jesus could use the generic in a special personal sense, could he have used it in its ordinary, biblical sense? Mark presents Jesus as using the generic sense of the expression, both in the singular (2:28) and in the plural (3:38). My basic point in this thread is that interpretation should not simply be a "majority rules" determination of what is the most common usage. Common usages, on account of their frequency, are an important criterion, but the local context of each use of the expression must take precedence. This is particularly the case when the majority of examples of the expression belong to quite a different usage, and when there were strong motivations for assimilating the exceptions to the general pattern (I have three possible motives for this in my last post and we can see this assimilation process at work in the redaction of Mark 2:28 and 3:38 in the other two synoptics). So the focus should be on the actual rhetorical construction and whether the generic or non-generic nuance makes the most sense of it. The non-generic reading appears to produce a non sequitur in the passage that would not otherwise exist.
No, native Greeks did not use the term "son of man"/"sons of men"; this is a Semiticism in the Greek that imperfectly expresses the idiom. The usage between the singular and plural also did not divide along the lines you've specified; both the singular and the plural could refer to humanity or human beings in general (whether in the generic "man, humankind" or in the indefinite "any person"). Some examples in Aramaic, Hebrew, and in Septuagintal Greek:
Sefire Inscription III.16-17: "If the idea comes to the heart of the kings of Arpad, in whatever way a son of man (br 'nsh, singular indefinite) dies, you are forsworn to all the gods of the treaty which is in this inscription".
Daniel 7:13: "In my vision at night I looked, and there before me was one like a son of man (br 'nsh, singular indefinite; huios anthrópou in the LXX), coming with the clouds of heaven".
4Q201 3:17: (= 1 Enoch 7:3): "Giants were born upon the earth in keeping with their infancy and grew at the rate of their growth and consumed the work of all the sons of men (bny 'nsh', plural generic, rendered as anthrópón in the Greek translation), but not were the men able to supply them".
4Q209 23:8: "And I saw three sections of the world: one for the sons of men (bny 'nsh', plural generic) to live in it; another for all the seas and the rivers, and another for the deserts".
Numbers 23:19 LXX (quoted in Philo of Alexandria, Vita Mosis 1.283): "God is not able to speak falsely as if he were a man (anthrópos, singular indefinite; 'ysh "man" in Hebrew), nor does he change his purpose like a son of man (huios anthrópou, singular indefinite; bn 'dm in Hebrew).
Job 25:6 (via Q11TgJob 9:9): "How much less man (= 'dm in the Hebrew, singular but with generic reference to humanity), who is but a maggot — a son of man (br 'nsh, singular generic), who is only a worm!"
Job 25:6 LXX: "But alas man (anthrópos) is but filth, and the son of man (huios anthrópou, singular generic) is but a maggot!"
1QapGen 21:13: "I shall make your descendants as numerous as the dust of the earth which no son of man (br 'nsh, singular indefinite) can number, so will your descendents be without number".
Psalm 8:4-5 LXX (quoted in Hebrews 2:6-7): "What is man (anthrópos, singular generic; = 'nsh in the Hebrew), that you think of him? The son of man (huios anthrópou, singular generic; = bn 'dm, singular generic) that you care for him? For you have made him a little lower than the angels and crowned him with glory and honor".
Psalm 144:3-4 LXX: "What is man (anthrópos, singular generic; = 'dm in the Hebrew), that you care for him? The son of man (huios anthrópou, singular generic; = bn 'nsh, singular generic) that you think of him? Man (anthrópos, singular generic; = 'dm in the Hebrew) is like a breath, his days are like a shadow that passes away".
Isaiah 51:12 LXX: "I, even I, am he who comforts you. Who are you that you fear mortal man (anthrópou thnétou, singular generic; = 'nwsh in Hebrew), the son of man (huios anthrópou, singular generic; = bn 'dm, singular generic), the ones (hoi, plural) who are but grass?"
4Q418 55:11: "Are they like a man ('nwsh, singular generic)? For he is lazy. And a son of man (bn 'dm, singular generic)? For he sits still".
1QS 3:13: "The Instructor should instruct and teach all the sons of light about the nature of all the sons of man (bny 'nsh, plural generic)".
Armazi Bilingual Inscription, lines 19-20: "Woe, woe to she who did not reach full age, incomplete, and so good and beautiful that no son of man (br 'ynsh, singular indefinite) was like her in goodness".
Tatian, Diatessaron (utilizing John 5:34-36 and via Ephraem, Commentary on the Diatessaron 13.10.3-5): " 'Now I do not accept testimony from the son of man (br nsh', singular generic, rendering the anthrópou in John 5:34-36) because I have a witness which is greater than that of John'. And if he did not receive witness from the son of man (br nsh', singular generic), why did John come first?"
Bardaisan, Liber Legum Regiorum 559.11-14: "This is the nature of the son of man (br nsh', singular generic), that he should be born and grow up and reach his peak and reproduce and grow old, while eating and drinking and sleeping and waking, and that he should die".
y. Shebbat 38d: "Nor even a bird perishes without the will of heaven. How much less the son of man (br nsh', singular generic; notice the qal wahomer argument)".
Genesis Rabbah 79:6: "Not even a bird is caught without the will of heaven. How much less the soul of the son of man (br nsh', singular generic)".