1. Are you talking about a texture for pupis? If so, put a stick texture tag on the eyes to make the texture move with the deformed geometry.
2. Heirarchy is important when you use deformers with HN. If you put your object and the deformer under the HN object at the same heirarchy level, the object is smoothed first and then the bend is applied. OTOH, if you parent the deformer to the object(or put both under a null and null under the HN), the bend is applied first and then the HN smoothing is applied to the bent object. Try changing up the heirarchy and see if that helps.