Is it dangerous to cover your whole head with the blanket as you sleep? I mean in terms of breathing. Someone I know insists on doing this.

Depends. If it is a child or adult who is unable to move the blanket away from his/her face when needed, there is the possibility of suffocation. If it is a normal adult, there should be no problem with this if your blanket allows enough airflow and/or you leave enough space for a hole to breath out of.