In use since the 1400s, "nasty" comes from the Arabic "niz'd" for "nest." Early bird watchers noticed that birds fouled their nests and called anything dirty "nesty" or "nasty." Eventually, the word extended to unpleasant situations and spiteful behavior.
Meanwhile, a "nester" is a derogatory term for a homesteader of the Old West who settled on grazing land used for cattle. The name derives from the patches of brush that settlers would stash around their vegetable gardens to protect them from weather and grazing animals.
The first use of the word "precocious" did not apply to children mature before their age. It applied to plants - specifically those that flower or set fruit before bearing leaves. In Europe, it's not unusual for precocious trees to have their spring in winter and, therefore, ripen early. Precocious, from the Latin "prae-" (before) and "coquere" (to cook), means cooked beforehand, or ripened before its time.
"Precocious figs" were first recorded in the 1600s. Centuries before, apricots, native to China, actually bore the name "praecoquum" (early ripe) because in their new location in the Mediterranean, they ripened earlier than the local peach.
SOURCES: 'Brewer's Dictionary of Prose and Fable,' revised by Ivor H. Evans; 'A Browser's Dictionary,' by John Ciardi; 'The Encyclopedia of Word and Phrase Origins,' by Robert Hendrickson; The World Book Dictionary.