Yaaa.. ST paid on Health Insurance will be eligible for exemption bcoz what we have to infer from Sec 80D is that any sum paid by the assessee to keep the premium in force shall be eligible for exemption...
Yes, as a health insurance policy, mediclaim also comes under tax deduction. Go for tax deducton if you already bought it. If you don't have mediclaim policy, go for it. It has some decent benefits over your health insurance policy and take some tax benefits too.