Definite article for masculine: ο
Ο άντρας = The man
Definite article for feminine: η
Η γυναίκα = The woman
Definite article for neuter: το
Το παιδί = The child
The indefinite article is the same as the number "one":
Indefinite article for masculine: ένας
Ένας άντρας = A man / One man
Indefinite article for feminine: μία / μια (*)
Μία γυναίκα = A woman / One woman
Indefinite article for neuter: ένα
Ένα παιδί = A child / One child
(*) Please note: The indefinite article for feminine could have an accent, or not. So you can see it as "μία" or as "μια". They both mean exactly the same and can be used in all contexts. You only change the way you read it. "Μία" is a disyllabic word (and you stretch on ι) while "μια" is monosyllabic (and you stretch on α).
No, ένας (masculine) and μία (feminine) mean "a(n)" or "one", i. e., the indefinite article. ο (masculine), η (feminine), and το (neuter) mean "the", i. e., the definite article. το does not necessarily refer to an object; for instance, "the child" is το παιδί, because it is a neuter noun.
Clearly, you're right on the etymology of gynecologic, LaP. But as for "vagina," my unabridged English dictionary states the English word goes back to its use in neo-Latin; and that it goes back to Latin "vāgina," where it meant "sheath"; and that's it, no "borrowed from Greek."
Also, the fact that modern Greek uses κόλπος or αιδοίο here suggests our English word comes from the Latin original.