The Conjuring 1 is indeed based on a real story. It's about the Perron family's experiences in a haunted farmhouse. The Warrens came to investigate the strange happenings like unexplained noises, objects moving on their own, and apparitions. Their investigations and the events they witnessed form the basis of the movie's story.
Yes. 'The Conjuring' series is inspired by real - life cases of the Warrens, who were paranormal investigators. The fourth movie likely draws from their files of investigations, though it may also take some creative liberties for the sake of cinematic storytelling.