My friend has been suffering from insomnia for a while. Are there any accounts in the Satcharita of Udi helping with sleep problems?

Yes, Chapter 33 provides specific examples of Sai Baba's Udi helping people with sleep issues. A footnote by R. Hari Sitaram Dixit mentions a friend who came to his office complaining that he had not been able to sleep for eight days, despite taking a doctor's medicine. After being given some of Maharaj's Udi and told to take it for three days, the friend reported back the very next day that he had slept very well throughout the night after taking it. The chapter also mentions a similar case of a child in Bandra who had not been able to sleep for two months. His father took him for Maharaj's Darshan in Shirdi, and that very night the child got sleep and continued to sleep well every night thereafter.