Now the real question is coming as "Should Facebook, even with some sort of "Child-friendly filter", be accessible to children" ?

IMHO, the answer is a red and clear NO, especially since Internet can really easily be a wild place in which any not-prepared person can easily get lost and make bad encounters.

It's a place accessible to everyone but the risks are often overlooked and the slightest bit of maturity would be expected from someone to use a computer, let alone access Internet.