Two hangings are shown in the film, in the style of a "long drop" designed to break the neck and cause instant death. This style was first introduced in the 1870's by William Marwood as a more humane approach. Before then, and certainly in 1828-1829 when the film was set, the victim was simply suspended by a rope around the neck, and choked to death by suffocation.
William Burke did not confess to the crimes in order to save his friends and love. He was actually betrayed by William Hare who sold him out after they were caught.