Did Sai Baba ask for money from his followers, and what was this practice called?

Yes, Sai Baba would frequently ask for offerings from those who came for his darshan. As described in Chapter 14, whether a person was Hindu, Muslim, or Parsi, Baba would ask them for Dakshina. This was not limited to small amounts; He might ask for anything from a few rupees to thousands or even lakhs, as He saw fit. This practice was a key part of the interaction with Him, and He would ask for Dakshina from anyone who came and bowed at His feet.