1) Zombies are fictional. That means they don't exist. That means if you want to write about zombies, you can make up your own rules.
2) Usually zombies are described as "undead", that is, they don't live at all.
3) to add to this answer,if we go according to zombie lore and movie lore . zombies are able to live as long as they have brains to eat, contrary to popular beliefs, zombies are not immortals.