1580s, "fruit of the mango-tree," which is extensively cultivated in India and other tropical countries, from Portuguese manga, from Malay (Austronesian) mangga and Tamil (Dravidian) mankay, from man "mango tree" + kay "fruit." Mango trees were brought from Timor to British gardens in Jamaica and St. Vincent 1793 by Capt. Bligh on his second voyage. Of the tree itself, by 1670s.
Old English mangere "merchant, trader, broker," agent noun from mangian "to traffic, trade," from Proto-Germanic *mangojan (source also of Old Saxon mangon, Old Norse mangari "monger, higgler"), from Latin mango (genitive mangonis) "dealer, trader, slave-dealer," which is related to mangonium "displaying of wares."
Not in Watkins or de Vaan, but Buck (with Tucker) describes it as "one who adorns his wares to give them an appearance of greater value" and writes it is probably a loan-word based on Greek manganon "means of charming or bewitching." Used in combinations in English at least since 12c. (fishmonger, cheesemonger, etc.); since 16c. chiefly with overtones of petty and disreputable (for example ballad-monger "inferior poet," 1590s; scandal-monger).
"military engine for hurling stones," mid-13c., from Old French mangonel "catapult, war engine for throwing stones, etc." (Modern French mangonneau), diminutive of Medieval Latin mangonum, from Vulgar Latin *manganum "machine," from Greek manganon "any means of tricking or bewitching," said to be from a PIE *mang- "to embellish, dress, trim" (source also of Old Prussian manga "whore," Middle Irish meng "craft, deception"), but Beekes thinks it might be Pre-Greek. Attested from c. 1200 in Anglo-Latin.