'Cotorra' is 'Parrot' in Spanish. So "The Parroting", but not in the sense of repeating things back.
Not sure about European Spanish, but cotorreo in spanish in Mexico and other parts of latin america means something like party, or reunion, hence what the post refers to as "the cotorreo". Nothing to do with parrots or parroting.
The name is definitely derived from "cotorra", and likely refers to the noisy chatter that wild groups of parrots have.
(Spanish here) Yep, it's used as in "lively chatter".
A 'cotorra' is a monk parakeet, and it's also used colloquially as "chatty person".
This is the right answer. Also used as "cotorreando".