That varies. New babies don't sleep through the night because they need to awaken to feed. As they get bigger, they sleep longer. Most babies can safely do an 8 hour stretch when they're several months old; some do it a little younger, some a little older. Babies are people; what happens one way in one happens a bit differently in another.
Varies. Sleeping thru the night can mean 6 hrs to some parents, and others 8 or even 10 hours. Some babies begin to sleep 6-8 hrs at 4 mo, most by 6 mo. Babies who learn the skill earlier have mastered the ability to fall asleep on their own. Put baby in bed while awake but drowsy, rather than rocking until sound asleep. Sweet dreams!