Do I need to be lead climbing to do the multipitch ice class?

Not necessarily but it is more helpful if you have some lead climbing experience. In instances where participants don't feel ready to lead we often use different toprope techniques to simulate a multipitch climb.

Do I need to learn to multipitch ice climb if I already know how to multipitch rock climb?

While multipitch rock climbing experience is beneficial there are more skills that go into multipitch ice climbing. Even a proficient rock climber with a lot of experience in rock terrain will benefit from gaining some ice specific knowledge.

Will rappelling be taught as part of the course?

What goes up must come down. We do cover rappelling in most multipitch ice clinics. Some of this is dependent on the venue and goals of the participants but since it's a fundamental aspect of completing a multipitch ice route we usually make a point to include it.