NG+ randomizes the world again, resets the quests and scales mobs (up to a maximum of lvl120). You get to keep Mapworks when you start a NG+ so you can always teleport there and farm some maps for items.
Enchantments, gems and overall luck with magical items.
Playing NG+ will increase the likelihood of getting one because Legendary items have relatively high level requirements.
Not sure. Just play the game as usual and keep your fingers crossed.