It's a...
telephone
Twelve smooth pebbles sit facing the sky,
it has 12 keys (including * and #)
With one large roof, keeping them dry.
(not sure) the plastic between keys themselves?
Listens and speaks at the same time,
Knows every secret, both yours and mine.
You can both talk and listen
Used by billions, invented by two,
Many people have telephones, but it was invented by Meucci and/or Graham Bell
Older than most, but wiser than few.
Everyone alive now was born after it was invented and it is not wise because it only transports voice, it's doesn't know anything