NEW YORK — Faith and survival, not the machinery of death, are the central themes at an atypical Holocaust museum in Brooklyn. The three-year-old Amud Aish Memorial Museum, located far from the tourist crowds at near the very edge of the borough, focuses on the experiences of Orthodox Jews during and after the Holocaust. Its collection includes letters, diaries, photos and religious items, like a frayed prayer shawl worn secretly by a prisoner at Auschwitz. Many were donated by Orthodox and ultra-Orthodox Jews who had stashed the artifacts in basements and attics would not have given them to another museum, Amud Aish staffers said. “Part of that is because their culture is different and they don’t patronize museums for the most part,” said Shoshana Greenwald, director of collections.