I will try to answer your queries, but as you are no doubt aware, these are very difficult questions. I also generally prefer social constructionism to essentialism, so I will not be giving a decidedly essentialist answer.

As Kenneth Dover and Michel Foucault showed many years ago, it is misleading to consider ancient sexuality in "our" categories and as you observed, the terminology reflects that mismatch (with a complex word field with contradictory usage, including agapê, eros, philia, himeros, pothos, and epithumia). James Davidson has further emphasized that we also need to be aware that the attitudes held by ancient Greeks changed over time and were contested within ancient Greek culture (or perhaps better: within Athenian culture, which produced the majority of our sources; e.g. Aristoph. Thesm. 49f.; 97f.; Plat. Leg. 636c, 835b-842a).

I am not certain there is currently a consensus on these complex issues, but I would say that the notion that there was a concept of a firm sexual orientation, let alone a group identity, should be abandoned, be it homo- or heterosexual. Even without such conceptual awareness there was of course a broad range of practice, both what we might call sensual and what we might term sexual. Practice is confirmed by a wealth of material (e.g. by vase painting, kalos inscriptions, myth, poetry and prose) and is not in question. The orthodoxy before Davidson, however, was that these practices were more about status than about pleasure, which is where pederasty comes in (active older men penetrating passive younger men as part of an erotic initiation rite). If I were pressed for a quantitative assessment, I would say that pederasty was probably the most common form of homosexual practice, though since it was clearly the form of practice with the most rules, history and interests tied to it, its quantitative predominance may be misleading.

Davidson looked beyond this orthodoxy and emphasized the genuine depth of connection between males found in myth and already in epic, so of sensuality, as being far more important an indicator that there was 'homosexuality' in ancient Greece (on a modified essentialist paradigm not focused on penetration). Given how intensely homosocial ancient Greek society was in many respects, this may well be a valuable path to take, but not everyone accepts Davidson's conclusions.

That said, I do not believe there is currently a satisfying paradigm to talk about these issues. The more one tries to pin these things down, the more one gets the sense that our material does not answer these questions and that we should hence try to modify our questions. If, however, someone with more experience can chime in, that would be welcome.

Bibliography

• Davidson, James, The Greeks and Greek love: a radical reappraisal of homosexuality in ancient Greece, London 2007.
• Dover, Kenneth J., Greek homosexuality, London 1978.
• Foucault, Michel, The history of sexuality. Vol. 2: the use of pleasure, trans. R. Hurley, New York 1985.
• Halperin, David M., Winkler, John J., and Zeitlin, Froma I., eds. Before sexuality: the construction of erotic experience in the ancient Greek world, Princeton 1992.
• Halperin, David M., How to do the history of homosexuality, Chicago 2002.