I think I do remember some of those spells he may have learned from Yubaba. There is one he used to distract those at the bridge; by blowing into his fingers, white petals fly out. He also used some type of restorative/boosting spell when he healed Chihiro who's unable to move her legs. I do think this is what enabled Chihiro to run at a faster speed than normal. Like  also said, he was able to temporarily suspend a frog in a dark water bubble. He was also able to render Chihiro invisible to the bathhouse staff while on the bridge, although I'm not sure if this is an effect of the earlier distraction spell or a new one altogether. Lastly, there was one a bit like telepathy, which he used to show Chihiro the way to Kamaji. Well, of course, all of these are just speculation on my part    