My friend brushed her teeth with backing soda, will that do any harm to a 14 year old girl?

Not at all. No it will not cause any harm to a 14 years old.It is an attractive option to toothpaste and it helps whiten the teeth and plaque removal.It is safely used by many and also available as baking soda tooth paste.
No. In the past baking soda was used to brush teeth. I might not use it all the time as it is more abrasive than traditional toothpaste.