Socrates had male suitors (
Alcibiades for instance), but he took the refreshingly modern view that the dynamic between a teacher and pupil should not be tainted by romance or sex. He was functionally abstinent as far as we can tell, or at least that's how he presented himself. You can see this in the way he's portrayed in
Symposium, which was written poshumously by Plato, one of his students (this is actually where the word "platonic" comes from). Note that Socrates' portrayal there was likely to be a little rosier than life, since part of Plato's purpose was to rid the damage done to Socrates' reputation when he was arrested for "corrupting the youth."
You're also right that intimacy between individuals of the same sex had a lot of particulars about what was considered appropriate and what was considered taboo. In a pederastic relationship, the erastes would seek the blessing of the eromenos' father. Eromenos were typically between the age of 14 and 20, while an erastes could be basically any age above that. Not all of these relationships were sexual; some followed the more Socratic ideal of a non-romantic master-apprentice dynamic, while others were more overtly sexual. The latter, while considered normal, still had a lot of caveats; only non-penetrative sex was considered honorable, because the Greeks (and many other cultures at that time) felt that to be penetrated was to be robbed of your manhood. While I'm sure it was codified into law in some places, it was mostly just a socially-enforced, cultural thing as far as I can tell. You're correct that it's not really the same thing as modern-day sexuality, because it wasn't an identity like being gay is today. It was mostly just a social institution, and one that was rightfully abolished to boot. Adults shouldn't be dating teenagers regardless of their gender.
Greeks didn't really view women as having sexual autonomy, so any kind of sex between women wasn't really thought of as
actual sex and was therefore irrelevant. Like, irrelevant to the point that very few surviving records describe it in the context of Greek culture, which is why people make such a big deal about Sappho.