The Essenes separated themselves from places like Jerusalem to set up a community free from the debauchery that as going on there such as their community leaders did not believe in giving orders to kill innocent children.
They taught chastity vowes, no oaths, new covenant, put extra emphasis on baptism, held all things in common, believed a leader should humble himself before a common person and much more. All things that Jesus and the 12 taught and did and they are the only other sect that practiced such things at the time of Jesus.
They thought they were the fulfillment of prophecy, not Jesus
Which the new covenant did they teach? The one to the houses of Judah and Israel does not exist yet
No they were not Christians, Christians didnt exist at the time of Jesus, the 12 and the Essenes.
And yes they vanished around 70 AD, the same time the church of Jerusalem (lead by James) vanished.