Can you describe some instances from the Sai Satcharitra where Sai Baba demonstrated his omniscience to his devotees?

Certainly. Chapter 28 of the Sai Satcharitra provides powerful examples of Sai Baba's ability to know the innermost thoughts and desires of his devotees. In one account, a devotee named Laxmichand privately worried that Baba's cough was the result of an evil eye. When he visited the masjid, Baba himself voiced the exact same thought, making Laxmichand realize that Baba dwells in everyone's heart. In another story from the same chapter, Baba appeared in a dream to a lady in Berhampur, asking for khichdi, even though she had never met him. This vision ultimately drew her and her husband to Shirdi, where Baba later accepted her offering with great delight, confirming the divine connection.