At what point in the boy's illness did the family hear about Sai Baba, and what did they hear about his powers?

The family heard about Sai Baba at a point of complete desperation. As narrated in Chapter 34, they had already tried every conceivable medical treatment for the boy's bone-cyst, including efforts by his doctor uncle, other physicians, and expert surgeons. After all these native and foreign treatments were exhausted without success, and even turning to their family gods seemed to bring no relief, word of Sai Baba reached their ears. They heard that a great saint, or 'Avaliya', lived in Shirdi who was so powerful he could heal diseases just with his sight. Crucially, they were told that if this King of Yogis applied Udi with his own hand, even incurable diseases would perish.