Some do, but have a separate deductible. The bottom line is that normal deliveries are generally not covered unless specifically stated that they are and a premium is charged for the benefit. Yes, with the permission of the guardian. Yes, if the child is out of state for school only and not a full time resident of the other state. The child returns home when school is not is session.
Some plans also cover missionaries.
Check with your agent. Here is what one insurer has to say.