Personne in the negative is a pronoun and as such its gender is masculine. Cf. http://forum.wordreference.com/showthread.php?t=751559
"Une personne intelligente peut apprendre une langue, mais personne ne peut apprendre toutes les langues." When "personne" means person, it's a feminine noun but when it means nobody it's masculine by default. Not quite the same, but "tour" feminine is tower while "tour" masculine is turn.
All French negatives are "double negatives". Ne + (pas, rien, personne, plus...)
"Everyone" would, I think, be "Tout le monde n'est pas parfait". And bear in mind that there's a difference even in English between "everyone is not perfect" (but some people are) and "no-one is perfect" (it's impossible).