Starting from bottom. By expressly mentioning fraud, Tasso again links Armida to Dante's Geryon (Inferno 17: 7), i.e. the Edenic Serpent, though Geryon has a male face because the devil adapts to circumstances. For an analysis of Geryon more in depth:
Armida's reference to "foreign climates," at first sight, simply means "all over the world," but there is a hidden hint at her own island in the Atlantic Ocean, a fake version of the Fortunate Isles whose legend was so often associated with the Discovery of America. See Umberto Eco, The Book of Legendary Lands, Rizzoli Ex Libris / International Publications, 2013. Or rather, Armida might imply this in Gerusalemme Liberata, but here, in the Conquistata reboot, her general headquarters are no longer set in an island.
In the first verse, Armida's speech is called "note" (plural). The term is polysemous. It can just be a more refined word for words, but more specifically it indicates musical notes, therefore suggesting her dangerousness as a mermaid. Still more specifically, in Renaissance parlance, "note" were the magic formulas and spells, so Armida's identity as a witch is here revealed too. But the knights, dazzled and charmed by love, won't notice all this.