Does having your child vaccinated against Rotavirus (the oral vaccine, Rotateq) make them immune to rotavirus?

Your second question is correct. It contains a live, weakened version of the virus so a healthy child can have an immune system response without actually getting sick. When a child does come into contact with this virus, a pool of antibodies are ready for it which most times prevents your child from being sick. At the very least, the vaccine will prevent your child from having a serious (ie fatal) case of it. I think my son's doctor said it prevents 98% of serious/fatal cases.