Do all Madrigals have a Fa-la-la chorus?

Answer 1

no, they don't. some funny ones by Orlando di Lasso have some interesting effect noises: the Echo song uses
two choruses, one to sing the song, one to be the echo.
Another one ( sorry, I blanked out on the title) is a barnyard song, and has the singers doing all sorts of animal noises, down to the hen laying an egg. Not a fa la to be heard!