^Yes. It is just that the dative case was lost following the terribly bad 'reformation' of the greek language in the early 70s. Along with the polytonic system.
Dative only survives in some phrases, mostly archaic, and is otherwise presented with a small periphrasis instead (in the case of the noun being 'Hellas', the periphrasis (not a case) with the same meaning as the dative would be 'στην Ελλάδα', while i now looked up the dative, which would have been -copy/pasting with polytonic...- 'τῇ Ἑλλάδι')
I think the case i numbered as 'third' is the accusative one, in greek it is termed as 'aitiatike'. Nominative more obviously is the 'onomastike', and yes, that is what i mean re 'Hellas' being in the nominative case, although some ultra language reformation weirdos would insist on using the same form in the accusative for many nouns in the nominative as well; it is very low practice, though, and thankfully mostly overruled by speakers themselves anyway.
Last case is the vocative i suppose, yes - "kletike" in greek. Used to pronounce someone, eg "Oh Agamemnon" etc.
Both dative and polytonic were still taught in schools here up until the start of the 70s, eg my mother learned the language with those as well. The reformation was hideous, but at least most of it was canceled in practice, cause it sounds so stupid

Supposedly it happened so as to limit the differences between use of the language by scholars and the more common use, and was an issue lingering on since the 1830s and the declaration of a new state of Greece. While the scholarly version is quite austere, the reform was not a good one. Anyway, that is an issue for another time...