What if the entire surface of the planet is destroed and no living thing survives except for whats in the vault?
If no one is there to jump start the life creation process, how is having this vault usefull?
There needs to be some sort of automatic incubation process that would bring the ova to maturity, allow growth of the embrio until a living, breathing human being pops out of a tank or something.
Hehe, you better also develop a robot that will teach those people about life or that living, breathing human isnt even going to know how to wipe its own butt much less restock the Earth.
Irrelevant.
Humans have evolved since the stone age, they can do it again.
True, but those humans had other humans to teach them, unless you are referring to the first two cavemen to ever exist. In this case everyone will be starting from nil in a room full of technology they couldnt possibly understand.