Botan has a few special abilities. She is able to fly on her oar, which is a traditional Japanese mode of transportation for mythical beings. She can also sense the spiritual energy of others and has some healing abilities.
As for her relationship with Yusuke, she acts as a mentor and guide to him throughout the series. They have a close relationship, but it is strictly platonic. Botan is often the voice of reason for Yusuke and helps keep him on track during his adventures.