The text says Sai Baba will serve the author in his home. Does this mean Baba performed household chores for Hemadpant?

While Chapter 2 does contain Sai Baba's promise, "Not just this story, but I shall serve in all ways in his home," this is not meant in the literal sense of performing household chores. The statement is part of a larger promise to give full assistance to a devotee who dissolves their ego and surrenders. This "service" implies a deeper, spiritual support and omnipresent grace in all aspects of the devotee's life, rather than physical labor. The core condition for this divine assistance, as mentioned in Chapter 2, is the complete dissolution of the ego.