You may buy your Medical insurance once the baby got a birth certificate. The reason is the company need your baby's name, DOB and the birth certificate number.
Yes, some of the products are true and some are not. Depends on what you want. i.e. Medical insurace for Clinic is must expensive than adult not more than 30 yrs old. The reason is the properbility of the kids visit the doctor is much more higher than youth.
However, If you are buying Life insurance, it will be cheaper than the adults.