What is the etymology of orichalchum, and is it related to chalk/talcum or calcite?

Wiktionary is your friend:

calx is probably from χάλιξ chalix: “pebble”:

Unknown, perhaps Pre-Greek. Probably cognate, ancestor, or descendant of Latin calx ‎(“limestone, chalk”)

χαλκός “copper”:

Uncertain. Has been compared to Proto-Slavic *želězo ‎(“iron”), Latin ferrum, and Hittite [script needed] ‎(ḫapalki-). Perhaps related to κάλχη ‎(kálkhē, “purple”). Ultimately, Proto-Indo-European origin seems unlikely and the word is probably a borrowing.

… So if calx is indeed from Greek, we have a non-Hellenic chalik– stem for “pebble”, and a non-Hellenic chalk– stem for “copper”.

We can’t rule out that they’re related somehow; and copper and limestone are both, um, minerals. But… probably not.

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