"Most Christian religions believe it will be a thousand-year period of peace"
While evangelicals, fundamentalists, charismatics, and Adventists often believe in a literal 1000 years, that is not the viewpoint of Catholics, Orthodox and Mainline Protestants who are amillennialist.
The idea only appears in Revelation, which was a latecomer in being accepted in the Bible canon, so much of it was not taken literally until after the Reformation.
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In regard JW beliefs: they teach that it is during this 1000 years that humanity will be restored to perfection. Nearly everyone who has ever died, perhaps as many as 20 billion people, will come back to life and be given a second change. The 1000 Years is Judgement Day. "New scrolls" will be open, the requirements which they will be judged by during the 1000 years.
Even though Revelation say that the dead are not brought to life until after the 1000 years, JWs teach that is not literal. They are "spiritually dead" until brought to perfection at the end of the 1000 years. Then they truly are alive in God's sight.
It's basically picking and choosing which parts to take literally and which to take symbolically.