When is it safe for my baby to sleep with a pillow?

No. No. Babies should not sleep with soft blankets, pillows or stuffed toys. They need a firm sleeping surface and should always be placed on their backs to sleep.
Never. There are safety issues with pillows and blankets. Only have your baby in the crib.
No. Young babies must not sleep with pillows. If an older baby sleep with pillows, the parents will worry off and on that something bad still might happen. Since babies don't need any pillows, it is best to not have pillows around sleeping babies.