This -idae is the plural of Latin -ides, a masculine patronymic (indicating "descent from"), from Greek -ides "son of," denoting descent from the person to whose name it is attached (such as Heraklides).
In astronomy, of meteor showers, "having its radiant in" the constellation named (Perseid, Leonid, etc.), it probably represents Latin -idis, from Greek -idos, the genitive of the feminine form of the patronymic suffix.
word-forming element, from Latin -farius, -fariam "in (so many) parts," as in bifariam "in two parts or places, in two ways;" multifariam "in many places," an element of disputed origin. Watkins suggests it is from PIE *dwi-dhe- "making two," from roots *dwi- "two" + *dhe- "to put, set." It also has been derived from Latin fari "to say" (as in nefarious), but de Vaan writes that "the alleged semantic development to 'in n ways' is obscure," and he points to the suggestion of a PIE *-dho-, with cognates in Sanskrit dvidha (adv.) "twofold;" tridha "threefold."
In paraphernalia, Mammalia, regalia, etc. it represents Latin or Greek -a (see -a (2)), plural suffix of nouns in -ium (Latin) or -ion (Greek), with formative or euphonic -i-.