Depends. That depends on the age of the kids, your health, and their need to know. Generally, an adult child should be aware of all significant family history to properly manage their own health status. If you are a recovered bulimic, it's ok. If you're an active bulimic and the children are not adult or mature, I would wait.
Depends. What you need to tell your children has a lot to do with the circumstances involved and the age and developmental level of your children. In general, younger children will be less understanding and more fearful, and any discussion should be limited or put on hold. Older children and teens may benefit from disucssing these issues, but be careful to not make them feel responsible for your health.